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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
solv-int/9407005 | Adam Doliwa | Adam Doliwa (Institute of Theoretical Physics, Warsaw University),
Paolo Maria Santini (Dipartimento di Fisica, Universita di Roma "La Sapienza"
and INFN Sezione di Roma) | Integrable dynamics of a discrete curve and the Ablowitz-Ladik hierarchy | LaTeX file, 14 pages + 4 figures | J. Math. Phys. 36 (1995) 1259 | 10.1063/1.531119 | IFT/6/94 | solv-int nlin.SI | null | We show that the following elementary geometric properties of the motion of a
discrete (i.e. piecewise linear) curve select the integrable dynamics of the
Ablowitz-Ladik hierarchy of evolution equations: i) the set of points
describing the discrete curve lie on the sphere S^3, ii) the distance between
any two subsequant points does not vary in time, iii) the dynamics does not
depend explicitly on the radius of the sphere. These results generalize to a
discrete context our previous work on continuous curves.
| [
{
"version": "v1",
"created": "Wed, 27 Jul 1994 19:34:43 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Doliwa",
"Adam",
"",
"Institute of Theoretical Physics, Warsaw University"
],
[
"Santini",
"Paolo Maria",
"",
"Dipartimento di Fisica, Universita di Roma \"La Sapienza\"\n and INFN Sezione di Roma"
]
] |
solv-int/9408001 | Hua Wu | Hua Wu and D. W. L. Sprung (Department of Physics and Astronomy,
McMaster University Hamilton, Ontario, Canada), J. Martorell (Dept.
d'Estructura i Constituents de la Materia, Facultat Fisica, University of
Barcelona, Spain) | Numerical investigation of iso-spectral cavities built from triangles | 15 pages, revtex, 5 postscript figures | null | 10.1103/PhysRevE.51.703 | null | solv-int nlin.SI | null | We present computational approaches as alternatives to the recent microwave
cavity experiment by S. Sridhar and A. Kudrolli (Phys. Rev. Lett. {\bf 72},
2175 (1994)) on iso-spectral cavities built from triangles. A straightforward
proof of iso-spectrality is given based on the mode matching method. Our
results show that the experiment is accurate to 0.3% for the first 25 states.
The level statistics resemble those of GOE when the integrable part of the
spectrum is removed.
| [
{
"version": "v1",
"created": "Wed, 17 Aug 1994 15:09:20 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Wu",
"Hua",
"",
"Department of Physics and Astronomy,\n McMaster University Hamilton, Ontario, Canada"
],
[
"Sprung",
"D. W. L.",
"",
"Department of Physics and Astronomy,\n McMaster University Hamilton, Ontario, Canada"
],
[
"Martorell",
"J.",
"",
"Dept.\n d'Estructura i Constituents de la Materia, Facultat Fisica, University of\n Barcelona, Spain"
]
] |
solv-int/9409001 | Frank Nijhoff | H.W. Capel and F.W. Nijhoff | Integrable Quantum Mappings | 13 pages, to appear in Proceedings of the Intl. Workshop on
Symmetries and Integrability of Difference Equations, eds. D. Levi, L. Vinet
and P. Winternitz | null | null | null | solv-int nlin.SI | null | We discuss the canonical structure of a class of integrable quantum mappings,
i.e. iterative canonical transformations that can be interpreted as a discrete
dynamical system. As particular examples we consider quantum mappings
associated with the lattice analogues of the KdV and MKdV equations. These
mappings possess a non-ultralocal quantum Yang-Baxter structure leading to the
existence of commuting families of exact quantum invariants. We derive the
associated quantum Miura transformations between these mappings and the
corresponding quantum bi-Hamiltonian structure.
| [
{
"version": "v1",
"created": "Fri, 2 Sep 1994 12:33:10 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Capel",
"H. W.",
""
],
[
"Nijhoff",
"F. W.",
""
]
] |
solv-int/9409002 | Dr "P. A" Clarkson | Andrew P. Bassom and Peter A. Clarkson (Department of Mathematics,
University of Exeter, Exeter, U.K.) | New exact solutions for the discrete fourth Painlev\'e equation | Tex file 14 pages | null | 10.1016/0375-9601(94)91294-7 | M27/94 (to be published in Physics Letters A) | solv-int nlin.SI | null | In this paper we derive a number of exact solutions of the discrete equation
$$x_{n+1}x_{n-1}+x_n(x_{n+1}+x_{n-1})=
{-2z_nx_n^3+(\eta-3\delta^{-2}-z_n^2)x_n^2+\mu^2\over
(x_n+z_n+\gamma)(x_n+z_n-\gamma)},\eqno(1)$$ where $z_n=n\delta$ and $\eta$,
$\delta$, $\mu$ and $\gamma$ are constants. In an appropriate limit (1) reduces
to the fourth \p\ (PIV) equation $${\d^2w\over\d z^2} = {1\over2w}\left({\d
w\over\d z}\right)^2+\tfr32w^3 + 4zw^2 + 2(z^2-\alpha)w +{\beta\over
w},\eqno(2)$$ where $\alpha$ and $\beta$ are constants and (1) is commonly
referred to as the discretised fourth Painlev\'e equation. A suitable
factorisation of (1) facilitates the identification of a number of solutions
which take the form of ratios of two polynomials in the variable $z_n$. Limits
of these solutions yield rational solutions of PIV (2). It is also known that
there exist exact solutions of PIV (2) that are expressible in terms of the
complementary error function and in this article we show that a discrete
analogue of this function can be obtained by analysis of (1).
| [
{
"version": "v1",
"created": "Fri, 16 Sep 1994 15:32:03 GMT"
}
] | 2015-06-26T00:00:00 | [
[
"Bassom",
"Andrew P.",
"",
"Department of Mathematics,\n University of Exeter, Exeter, U.K."
],
[
"Clarkson",
"Peter A.",
"",
"Department of Mathematics,\n University of Exeter, Exeter, U.K."
]
] |
solv-int/9409003 | Dr "P. A" Clarkson | Peter A. Clarkson and Elizabeth L. Mansfield (Department of
Mathematics, University of Exeter, Exeter, U.K.) | Symmetry Reductions and Exact Solutions of Shallow Water Wave Equations | Tex file 19 pages, figures available from author | null | null | M94/36, Department of Mathematics, University of Exeter | solv-int nlin.SI | null | In this paper we study symmetry reductions and exact solutions of the shallow
water wave (SWW) equation $$u_{xxxt} + \alpha u_x u_{xt} + \beta u_t u_{xx} -
u_{xt} - u_{xx} = 0,\eqno(1)$$ where $\alpha$ and $\beta$ are arbitrary,
nonzero, constants, which is derivable using the so-called Boussinesq
approximation. Two special cases of this equation, or the equivalent nonlocal
equation obtained by setting $u_x=U$, have been discussed in the literature.
The case $\alpha=2\beta$ was discussed by Ablowitz, Kaup, Newell and Segur
[{\it Stud.\ Appl.\ Math.}, {\bf53} (1974) 249], who showed that this case was
solvable by inverse scattering through a second order linear problem. This case
and the case $\alpha=\beta$ were studied by Hirota and Satsuma [{\it J.\ Phys.\
Soc.\ Japan}, {\bf40} (1976) 611] using Hirota's bi-linear technique. Further
the case $\alpha=\beta$ is solvable by inverse scattering through a third order
linear problem. In this paper a catalogue of symmetry reductions is obtained
using the classical Lie method and the nonclassical method due to Bluman and
Cole [{\it J.\ Math.\ Mech.\/}, {\bf 18} (1969) 1025]. The classical Lie method
yields symmetry reductions of (1) expressible in terms of the first, third and
fifth \p\ transcendents and Weierstrass elliptic functions. The nonclassical
method yields a plethora of exact solutions of (1) with $\alpha=\beta$ which
possess a rich variety of qualitative behaviours. These solutions all like a
two-soliton solution for $t<0$ but differ radically for $t>0$ and may be viewed
as a nonlinear superposition of two solitons, one travelling to the left with
arbitrary speed and the other to the right with equal and opposite speed.
| [
{
"version": "v1",
"created": "Fri, 23 Sep 1994 13:14:21 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Clarkson",
"Peter A.",
"",
"Department of\n Mathematics, University of Exeter, Exeter, U.K."
],
[
"Mansfield",
"Elizabeth L.",
"",
"Department of\n Mathematics, University of Exeter, Exeter, U.K."
]
] |
solv-int/9409004 | Yavuz Nutku | E. V. Ferapontov and Y. Nutku | On the Monge-Ampere equivalent of the sine-Gordon equation | latex | null | 10.1088/0305-4470/27/23/026 | null | solv-int nlin.SI | null | Surfaces of constant negative curvature in Euclidean space can be described
by either the sine-Gordon equation for the angle between asymptotic directions,
or a Monge-Ampere equation for the graph of the surface. We present the
explicit form of the correspondence between these two integrable non-linear
partial differential equations using their well-known properties in
differential geometry. We find that the cotangent of the angle between
asymptotic directions is directly related to the mean curvature of the surface.
This is a Backlund-type transformation between the sine-Gordon and Monge-Ampere
equations.
| [
{
"version": "v1",
"created": "Mon, 3 Oct 1994 08:55:56 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Ferapontov",
"E. V.",
""
],
[
"Nutku",
"Y.",
""
]
] |
solv-int/9410001 | Nimmo Jjc | J J C NIMMO(Department of Mathematics, University of Glasgow, Glasgow
G12 8QW, Scotland) | Darboux Transformations from Reductions of the KP Hierarchy | 10 pages, LaTeX2e plus Latex2e style file for layout. (Should work
with LaTeX209 with minimum changes (see line 3 of source)) | null | null | University of Glasgow, Department of Mathematics, Paper No. 94/54 | solv-int nlin.SI | null | The use of effective Darboux transformations for general classes Lax pairs is
discussed. The general construction of ``binary'' Darboux transformations
preserving certain properties of the operator, such as self-adjointness, is
given. The classes of Darboux transformations found include the multicomponent
BKP and CKP reductions of the KP hierarchy.
| [
{
"version": "v1",
"created": "Tue, 11 Oct 1994 16:10:47 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"NIMMO",
"J J C",
"",
"Department of Mathematics, University of Glasgow, Glasgow\n G12 8QW, Scotland"
]
] |
solv-int/9410002 | Troy Shinbrot | Troy Shinbrot (Northwestern University), J.M. Ottino (Northwestern
University) | Maps, PDE's and Solitary Waves | 28 pages, Binhexed Macintosh MS Word 5.1 file follows; available in
hardcopy by request ([email protected]). In press: Int. J. Bif. &
Chaos | null | 10.1142/S0218127495000429 | null | solv-int chao-dyn nlin.CD nlin.PS nlin.SI patt-sol | null | We describe a map-based model which reproduces many of the behaviors seen in
partial differential equations (PDE's). Like PDE's, we show that this model can
support an infinite number of stationary solutions, traveling solutions,
breathing solutions, and elastically colliding solutions. Unlike PDE's, the
model can be applied with minimal computational machinery, and few sources of
numerical error. Moreover, this model clarifies possible mechanisms by which
various coherent solutions are maintained in the face of dispersion.
| [
{
"version": "v1",
"created": "Thu, 13 Oct 1994 21:58:42 GMT"
}
] | 2015-06-26T00:00:00 | [
[
"Shinbrot",
"Troy",
"",
"Northwestern University"
],
[
"Ottino",
"J. M.",
"",
"Northwestern\n University"
]
] |
solv-int/9410003 | Grinevich Piotr | Piotr G.Grinevich and Roman G.Novikov | Transparent Potentials at Fixed Energy in Dimension Two. Fixed-Energy
Dispersion Relations for the Fast Decaying Potentials | 38 pages, TeX | null | 10.1007/BF02099609 | null | solv-int funct-an hep-th math.FA nlin.SI | null | For the two-dimensional Schr\"odinger equation $$ [- \Delta
+v(x)]\psi=E\psi,\ x\in \R^2,\ E=E_{fixed}>0 \ \ \ \ \ (*)$$ at a fixed
positive energy with a fast decaying at infinity potential $v(x)$ dispersion
relations on the scattering data are given.Under "small norm" assumption using
these dispersion relations we give (without a complete proof of sufficiency) a
characterization of scattering data for the potentials from the Schwartz class
$S=C_{\infty}^{(\infty)} (\hbox{\bf R}^2).$ For the potentials with zero
scattering amplitude at a fixed energy $\scriptstyle E_{fixed}$ (transparent
potentials) we give a complete proof of this characterization. As a consequence
we construct a family (parameterized by a function of one variable) of
two-dimensional spherically-symmetric real potentials from the Schwartz class
$S$ transparent at a given energy. For the two-dimensional case (without
assumption that the potential is small) we show that there are no nonzero real
exponentially decreasing at infinity, potentials transparent at a fixed energy.
For any dimension greater or equal 1 we prove that there are no nonzero real
potentials with zero forward scattering amplitude at an energy interval. We
show that KdV-type equations in dimension 2+1 related with the scattering
problem $(*)$ (the Novikov-Veselov equations) do not preserve, in general,
these dispersion relations starting from the second one. As a corollary these
equations do not preserve, in general , the decay rate faster then $|x|^{-3}$
for initial data from the Schwartz class.
| [
{
"version": "v1",
"created": "Wed, 26 Oct 1994 10:53:46 GMT"
},
{
"version": "v2",
"created": "Fri, 28 Oct 1994 18:04:49 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Grinevich",
"Piotr G.",
""
],
[
"Novikov",
"Roman G.",
""
]
] |
solv-int/9410004 | null | Steven Nerney ( National Research Council Associate, NASA-Marshall
Space Flight Center, Alabama 35812), Edward J. Schmahl (Astronomy Department,
University of Maryland, College Park, MD 20742) and Z. E. Musielak
(Department of Mechanical and Aerospace Engineering, and Center for Space
Plasmas and Aeronomic Research, University of Alabama at Huntsville,
Huntsville, Alabama 35899) | Analytic Solutions of the Vector Burgers' Equation | one postscript figure (22K) appended to paper | null | null | 93-120 | solv-int nlin.SI | null | The well-known analytical solution of Burgers' equation is extended to
curvilinear coordinate systems in three-dimensions by a method which is much
simpler and more suitable to practical applications than that previously used.
The results obtained are applied to incompressible flow with cylindrical
symmetry, and also to the decay of an initially linearly increasing wind.
| [
{
"version": "v1",
"created": "Tue, 1 Nov 1994 16:05:51 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Nerney",
"Steven",
"",
"National Research Council Associate, NASA-Marshall\n Space Flight Center, Alabama 35812"
],
[
"Schmahl",
"Edward J.",
"",
"Astronomy Department,\n University of Maryland, College Park, MD 20742"
],
[
"Musielak",
"Z. E.",
"",
"Department of Mechanical and Aerospace Engineering, and Center for Space\n Plasmas and Aeronomic Research, University of Alabama at Huntsville,\n Huntsville, Alabama 35899"
]
] |
solv-int/9411001 | Metin Gurses | Burak Gurel, Metin Gurses and Ismagil Habibullin | Boundary Value Problems For Integrable Equations Compatible With The
Symmetry Algebra | 25 pages , Latex , no figures | null | 10.1063/1.531189 | null | solv-int nlin.SI | null | Boundary value problems for integrable nonlinear partial differential
equations are considered from the symmetry point of view. Families of boundary
conditions compatible with the Harry-Dym, KdV and MKdV equations and the
Volterra chain are discussed. We also discuss the uniqueness of some of these
boundary conditions.
| [
{
"version": "v1",
"created": "Wed, 9 Nov 1994 10:40:03 GMT"
},
{
"version": "v2",
"created": "Thu, 10 Nov 1994 07:36:56 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Gurel",
"Burak",
""
],
[
"Gurses",
"Metin",
""
],
[
"Habibullin",
"Ismagil",
""
]
] |
solv-int/9411002 | Sergej Flach | S. Flach | On the Existence of Localized Excitations in Nonlinear Hamiltonian
Lattices | 13 pages, LaTeX, 2 figures will be mailed upon request (Phys. Rev. E,
in press) | null | 10.1103/PhysRevE.51.1503 | null | solv-int nlin.SI | null | We consider time-periodic nonlinear localized excitations (NLEs) on
one-dimensional translationally invariant Hamiltonian lattices with arbitrary
finite interaction range and arbitrary finite number of degrees of freedom per
unit cell. We analyse a mapping of the Fourier coefficients of the NLE
solution. NLEs correspond to homoclinic points in the phase space of this map.
Using dimensionality properties of separatrix manifolds of the mapping we show
the persistence of NLE solutions under perturbations of the system, provided
NLEs exist for the given system. For a class of nonintegrable Fermi-Pasta-Ulam
chains we rigorously prove the existence of NLE solutions.
| [
{
"version": "v1",
"created": "Mon, 14 Nov 1994 23:25:24 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Flach",
"S.",
""
]
] |
solv-int/9411003 | Jarmo Hietarinta | J. Hietarinta (Department of Physics, University of Turku, 20500
Turku, Finland), B. Grammaticos (LPN, Universite Paris VII, Tour 24-14, 5eme
etage, 75251 Paris, France) and A. Ramani (CPT, Ecole Polytechnique, 91128
Palaiseau, France) | Integrable Trilinear PDE's | 10 pages in plain TeX | null | null | null | solv-int nlin.SI | null | In a recent publication we proposed an extension of Hirota's bilinear
formalism to arbitrary multilinearities. The trilinear (and higher) operators
were constructed from the requirement of gauge invariance for the nonlinear
equation. Here we concentrate on the trilinear case, and use singularity
analysis in order to single out equations that are likely to be integrable. New
PDE's are thus obtained, along with others already well-known for their
integrability and for which we obtain here the trilinear expression. To appear
in the proceedings of NEEDS'94 (11-18 September, Los Alamos)
| [
{
"version": "v1",
"created": "Wed, 16 Nov 1994 15:06:05 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Hietarinta",
"J.",
"",
"Department of Physics, University of Turku, 20500\n Turku, Finland"
],
[
"Grammaticos",
"B.",
"",
"LPN, Universite Paris VII, Tour 24-14, 5eme\n etage, 75251 Paris, France"
],
[
"Ramani",
"A.",
"",
"CPT, Ecole Polytechnique, 91128\n Palaiseau, France"
]
] |
solv-int/9411004 | Metin Gurses | Metin Gurses and Atalay Karasu | Variable Coefficient Third Order KdV Type of Equations | Latex file , 15 pages | null | 10.1063/1.530974 | null | solv-int nlin.SI | null | We show that the integrable subclassess of a class of third order
non-autonomous equations are identical with the integrable subclassess of the
autonomous ones.
| [
{
"version": "v1",
"created": "Wed, 16 Nov 1994 14:28:19 GMT"
},
{
"version": "v2",
"created": "Thu, 17 Nov 1994 08:52:42 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Gurses",
"Metin",
""
],
[
"Karasu",
"Atalay",
""
]
] |
solv-int/9411005 | null | Steven Nerney (National Research Council Associate, NASA-Marshall
Space Flight Center, Alabama 35812), Edward J. Schmahl (Astronomy Department,
University of Maryland, College Park, MD 20742) and Z. E. Musielak
(Department of Mechanical and Aerospace Engineering, and Center for Space
Plasmas and Aeronomic Research, University of Alabama at Huntsville,
Huntsville, Alabama 35899) | Limits to Extensions of Burgers Equation | Plain Tex, no figures | null | null | 94-107 | solv-int astro-ph chao-dyn comp-gas nlin.CD nlin.CG nlin.SI | null | The vector Burgers equation is extended to include pressure gradients and
gravity. It is shown that within the framework of the Cole-Hopf transformation
there are no physical solutions to this problem. This result is important
because it clearly demonstrates that any extension of Burgers equation to more
interesting physical situations is strongly limited.
| [
{
"version": "v1",
"created": "Thu, 17 Nov 1994 22:33:09 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Nerney",
"Steven",
"",
"National Research Council Associate, NASA-Marshall\n Space Flight Center, Alabama 35812"
],
[
"Schmahl",
"Edward J.",
"",
"Astronomy Department,\n University of Maryland, College Park, MD 20742"
],
[
"Musielak",
"Z. E.",
"",
"Department of Mechanical and Aerospace Engineering, and Center for Space\n Plasmas and Aeronomic Research, University of Alabama at Huntsville,\n Huntsville, Alabama 35899"
]
] |
solv-int/9411006 | Kenji Kajiwara | Y.Ohta(Dept. Appl. Math., Hiroshima Univ.), K.Kajiwara(Dept. Elecrical
Eng., Doshisha Univ.), and J.Satsuma(Dept. Math. Sci., Univ. Tokyo) | Bilinear Structure and Exact Solutions of the Discrete Painlev\'e I
Equation | 6 pages in LaTeX, to appear in Proceedings of the Workshop on
Symmetries and Integrability of Difference Equations, CRM Proceedings and
Lecture Notes Series, AMS, 1994 | null | null | null | solv-int hep-th nlin.SI | null | Bilinear structure for the discrete Painlev\'e I equation is investigated.
The solution on semi-infinite lattice is given in terms of the Casorati
determinant of discrete Airy function. Based on this fact, the discrete
Painlev\'e I equation is naturally extended to a discrete coupled system.
Corresponding matrix model is also mentioned.
| [
{
"version": "v1",
"created": "Wed, 30 Nov 1994 06:09:34 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Ohta",
"Y.",
"",
"Dept. Appl. Math., Hiroshima Univ."
],
[
"Kajiwara",
"K.",
"",
"Dept. Elecrical\n Eng., Doshisha Univ."
],
[
"Satsuma",
"J.",
"",
"Dept. Math. Sci., Univ. Tokyo"
]
] |
solv-int/9412001 | R. A. Sharipov | R.A. Sharipov (Dep. of Math., Bashkir State University, Ufa, Russia),
R.I. Yamilov (Inst. of Math. UrO RAN, Chernishevsky 112, Ufa, Russia) | B\"acklund transformation and the construction of the integrable
boundary-value problem for the equation $u_{xx}-u_{tt}=e^u-e^{-2u}$ | 7 pages AmS-TeX, Published in book: Problems of Math. Physics and the
asymptotics of their solutions, (V.Yu. Novokshenov, ed.) Inst. of Math. UrO
AN SSSR, Ufa, 1991, pp. 66-77 | null | null | null | solv-int nlin.SI | null | B\"acklund transformation for the Bullough-Dodd-Jiber-Shabat equation
$u_{xx}-u_{tt}=e^u-e^{-2u}$ is found. The construction of integrable boundary
condition for this equation together with the algebro-geometric solutions
satisfying it are suggested.
| [
{
"version": "v1",
"created": "Mon, 5 Dec 1994 05:33:27 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Sharipov",
"R. A.",
"",
"Dep. of Math., Bashkir State University, Ufa, Russia"
],
[
"Yamilov",
"R. I.",
"",
"Inst. of Math. UrO RAN, Chernishevsky 112, Ufa, Russia"
]
] |
solv-int/9412002 | Dr "P. A" Clarkson | Peter A. Clarkson and Andrew P. Bassom (Department of Mathematics,
University of Exeter, Exeter, U.K.) | Backlund Transformations and Hierarchies of Exact Solutions for the
Fourth Painleve Equation and their Application to Discrete Equations | Tex file 13 pages | null | null | M94/42, Department of Mathematics, University of Exeter | solv-int nlin.SI | null | In this paper we describe B\"acklund transformations and hierarchies of exact
solutions for the fourth Painlev\'e equation (PIV) $${\d^2 w\over\d
z^2}={1\over2w}\left(\d w\over\d z\right)^2 + {{3\over2}}w^3 + 4zw^2 +
2(z^2-\alpha)w+{\beta\over w},\eqno(1){\hbox to 16pt{\hfill}}$$ with $\alpha$,
$\beta$ constants. Specifically, a nonlinear superposition principle for PIV,
hierarchies of solutions expressible in terms of complementary error or
parabolic cylinder functions as well as rational solutions will be derived.
Included amongst these hierarchies are solutions of (1) for which
$\alpha=\pm\tfr12n$ and $\beta=-\tfr12n^2$, with $n$ an integer. These
particular forms arise in quantum gravity and also satisfy a discrete analogue
of the first Painlev\'e equation. We also obtain a number of exact solutions of
the discrete fourth Painlev\'e equation $$x_{n+1}x_{n-1}+x_n(x_{n+1}+x_{n-1})=
{-2z_nx_n^3+(\eta-3\delta^{-2}-z_n^2)x_n^2+\mu^2\over
(x_n+z_n+\gamma)(x_n+z_n-\gamma)},\eqno(2){\hbox to 16pt{\hfill}}$$}%
{\narrower\noindent\baselineskip=12pt where $z_n=n\delta$ and $\eta$, $\delta$,
$\mu$ and $\gamma$ are constants, which, in an appropriate limit, reduces to
PIV (1). A suitable factorisation of (2) facilitates the identification of a
number of solutions which take the form of ratios of two polynomials in the
variable $z_n$ and the limits of these solutions yield rational solutions of
(1).
| [
{
"version": "v1",
"created": "Fri, 9 Dec 1994 11:48:03 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Clarkson",
"Peter A.",
"",
"Department of Mathematics,\n University of Exeter, Exeter, U.K."
],
[
"Bassom",
"Andrew P.",
"",
"Department of Mathematics,\n University of Exeter, Exeter, U.K."
]
] |
solv-int/9412003 | Dr "P. A" Clarkson | P.A. Clarkson, E.L. Mansfield and A.E. Milne (Department of
Mathematics, University of Exeter, Exeter, U.K.) | Symmetries and Exact Solutions of a 2+1-dimensional Sine-Gordon System | Tex file 22 pages, figures available from author | null | null | M94/44, Department of Mathematics, University of Exeter | solv-int nlin.SI | null | We investigate the classical and nonclassical reductions of the
$2+1$-dimensional sine-Gordon system of Konopelchenko and Rogers, which is a
strong generalisation of the sine-Gordon equation. A family of solutions
obtained as a nonclassical reduction involves a decoupled sum of solutions of a
generalised, real, pumped Maxwell-Bloch system. This implies the existence of
families of solutions, all occurring as a decoupled sum, expressible in terms
of the second, third and fifth Painlev\'e transcendents, and the sine-Gordon
equation. Indeed, hierarchies of such solutions are found, and explicit
transformations connecting members of each hierarchy are given. By applying a
known B\"acklund transformation for the system to the new solutions found, we
obtain further families of exact solutions, including some which are expressed
as the argument and modulus of sums of products of Bessel functions with
arbitrary coefficients. Finally, we prove the sine-Gordon system has the
Painlev\'e property, which requires the usual test to be modified, and derive a
non-isospectral Lax pair for the generalised, real, pumped Maxwell-Bloch
system.
| [
{
"version": "v1",
"created": "Fri, 9 Dec 1994 13:13:14 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Clarkson",
"P. A.",
"",
"Department of\n Mathematics, University of Exeter, Exeter, U.K."
],
[
"Mansfield",
"E. L.",
"",
"Department of\n Mathematics, University of Exeter, Exeter, U.K."
],
[
"Milne",
"A. E.",
"",
"Department of\n Mathematics, University of Exeter, Exeter, U.K."
]
] |
solv-int/9412004 | Kenji Kajiwara | Kenji Kajiwara(Dept. Electrical Eng., Doshisha Univ.), Yasuhiro
Ohta(Dept. Appl. Math., Fac. Eng., Hiroshima Univ.), and Junkichi
Satsuma(Dept. Math. Sci., Univ. of Tokyo) | Casorati Determinant Solutions for the Discrete Painlev\'e III Equation | 16 pages in LaTeX | null | 10.1063/1.531353 | null | solv-int hep-th nlin.SI | null | The discrete Painlev\'e III equation is investigated based on the bilinear
formalism. It is shown that it admits the solutions expressed by the Casorati
determinant whose entries are given by the discrete Bessel function. Moreover,
based on the observation that these discrete Bessel functions are transformed
to the $q$-Bessel functions by a simple variable transformation, we present a
$q$-difference analogue of the Painlev\'e III equation.
| [
{
"version": "v1",
"created": "Thu, 15 Dec 1994 07:47:05 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Kajiwara",
"Kenji",
"",
"Dept. Electrical Eng., Doshisha Univ."
],
[
"Ohta",
"Yasuhiro",
"",
"Dept. Appl. Math., Fac. Eng., Hiroshima Univ."
],
[
"Satsuma",
"Junkichi",
"",
"Dept. Math. Sci., Univ. of Tokyo"
]
] |
solv-int/9412005 | null | P.G.Grinevich (Landau Institute for Theoretical Physics, Kosygina 2,
Moscow, Russia.), M.U.Schmidt (Institut f\"ur Theoretische Physik, Freie
Universit\"at Berlin, Arnimallee 14 - Berlin, Germany) | Period preserving nonisospectral flows and the moduli space of periodic
solutions of soliton equations | 35 pages, LaTex. Macros file elsart.sty is used (it was submitted by
the authors to [email protected] library macroses),e-mail:
[email protected], e-mail:[email protected] | Physica D Nr. 87, pp. 73-98 (1995) | 10.1016/0167-2789(95)00139-U | null | solv-int hep-th nlin.SI | null | Flows on the moduli space of the algebraic Riemann surfaces, preserving the
periods of the corresponding solutions of the soliton equations are studied. We
show that these flows are gradient with respect to some indefinite symmetric
flat metric arising in the Hamiltonian theory of the Whitham equations. The
functions generating these flows are conserved quantities for all the equations
simultaneously. We show that for 1+1 systems these flows can be imbedded in a
larger system of ordinary nonlinear differential equations with a rational
right-hand side. Finally these flows are used to give a complete description of
the moduli space of algebraic Riemann surfaces corresponding to periodic
solutions of the nonlinear Schr\"odinger equation.
| [
{
"version": "v1",
"created": "Thu, 15 Dec 1994 14:11:22 GMT"
},
{
"version": "v2",
"created": "Fri, 16 Dec 1994 20:04:23 GMT"
},
{
"version": "v3",
"created": "Thu, 25 May 1995 10:43:25 GMT"
}
] | 2016-01-19T00:00:00 | [
[
"Grinevich",
"P. G.",
"",
"Landau Institute for Theoretical Physics, Kosygina 2,\n Moscow, Russia."
],
[
"Schmidt",
"M. U.",
"",
"Institut für Theoretische Physik, Freie\n Universität Berlin, Arnimallee 14 - Berlin, Germany"
]
] |
solv-int/9412006 | null | Martin U. Schmidt | Integrable systems and Riemann surfaces of infinite genus | 91 page, LaTeX, no pictures | Memoirs of the AMS Nr 581 (1996) | null | SFB 288/102 | solv-int hep-th nlin.SI | null | To the spectral curves of smooth periodic solutions of the $n$-wave equation
the points with infinite energy are added. The resulting spaces are considered
as generalized Riemann surfcae. In general the genus is equal to infinity,
nethertheless these Riemann surfaces are similar to compact Riemann surfaces.
After proving a Riemann Roch Theorem we can carry over most of the
constructions of the finite gap potentials to all smooth periodic potentials.
The symplectic form turns out to be closely related to Serre duality. Finally
we prove that all non-linear PDE's, which belong to the focussing case of the
non-linear Schr\"odinger equation, have global solutions for arbitrary smooth
periodic inital potantials.
| [
{
"version": "v1",
"created": "Wed, 21 Dec 1994 19:33:32 GMT"
}
] | 2016-01-19T00:00:00 | [
[
"Schmidt",
"Martin U.",
""
]
] |
solv-int/9412007 | Jarmo Niilo Olavi Hietarinta | J. Satsuma, K. Kajiwara, B. Grammaticos, J. Hietarinta and A. Ramani | Bilinear Discrete Painleve-II and its Particular Solutions | 9 pages in plain TeX | null | 10.1088/0305-4470/28/12/025 | null | solv-int nlin.SI | null | By analogy to the continuous Painlev\'e II equation, we present particular
solutions of the discrete Painlev\'e II (d-P$\rm_{II}$) equation. These
solutions are of rational and special function (Airy) type. Our analysis is
based on the bilinear formalism that allows us to obtain the $\tau$ function
for d-P$\rm_{II}$. Two different forms of bilinear d-P$\rm_{II}$ are obtained
and we show that they can be related by a simple gauge transformation.
| [
{
"version": "v1",
"created": "Fri, 23 Dec 1994 12:26:34 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Satsuma",
"J.",
""
],
[
"Kajiwara",
"K.",
""
],
[
"Grammaticos",
"B.",
""
],
[
"Hietarinta",
"J.",
""
],
[
"Ramani",
"A.",
""
]
] |
solv-int/9501001 | Adam Doliwa | Adam Doliwa (Institute of Theoretical Physics, Warsaw University),
Paolo Maria Santini (Dipartimento di Fisica, Universita di Catania and INFN
Sezione di Roma) | The Integrable Dynamics of Discrete and Continuous Curves | 12 pages, LaTeX file, 4 ps figures | null | null | Warsaw University IFT 22/94 | solv-int nlin.SI | null | We show that the following geometric properties of the motion of discrete and
continuous curves select integrable dynamics: i) the motion of the curve takes
place in the N dimensional sphere of radius R, ii) the curve does not stretch
during the motion, iii) the equations of the dynamics do not depend explicitly
on the radius of the sphere. Well known examples of integrable evolution
equations, like the nonlinear Schroedinger and the sine-Gordon equations, as
well as their discrete analogues, are derived in this general framework.
| [
{
"version": "v1",
"created": "Fri, 30 Dec 1994 20:45:31 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Doliwa",
"Adam",
"",
"Institute of Theoretical Physics, Warsaw University"
],
[
"Santini",
"Paolo Maria",
"",
"Dipartimento di Fisica, Universita di Catania and INFN\n Sezione di Roma"
]
] |
solv-int/9501002 | Piotr Grinevich | P.G.Grinevich, S.P.Novikov | String equation--2. Physical solution | 32 pages, LaTex, 4 pictures in separate files. Subj-class and
Journal-ref added | Algebra and Analysis v. 6 No. 3 (1994) 118-140 (in russian);
english translation -- St. Petersburg Math. J. v. 6 No. 3 (1995) 553-574 | null | null | solv-int hep-th nlin.SI | null | This paper is a continuation of the paper by S.P.Novikov in Funct.Anal.Appl.,
v.24(1990), No 4, pp 196-206. String equation is by definition the equation
$[L,A]=1$ for the coefficients of two linear ordinary differential operators
$L$ and $A$. For the ``double scaling limit'' of the matrix model we always
have $L=-\partial_x^2+u(x)$, $A$ is some differential operator of the odd order
$2k+1$. In the first nontrivial case $k=1$ we have the Painelev\'e-1 (P-1)
equation. Only special real ``separatrix'' solutions of P-1 are important in
the quantum field theory. By the conjecture of Novikov these ``physical''
solutions, which are analytically exceptional probably have much stronger
symmetry then the other solutions but it is not proved until now. Two
asymptotic methods were developed in the previous paper -- nonlinear
semiclassics (or the Bogolubov-Whitham averaging method) and the linear
semiclassics for the ``Isomonodromic'' method. The nonlinear semiclassics gives
a good approximation for the general (``non-physical'') solutions of P-1 but
fails in the ``physical'' case. In our paper the linear semiclasics for the
``physical'' solutions of the P-1 equations is studied. In particular
connection between the semiclassics on Riemann surfaces and Hamiltonian
foliations on these surfaces is established.
| [
{
"version": "v1",
"created": "Wed, 11 Jan 1995 20:16:04 GMT"
},
{
"version": "v2",
"created": "Fri, 11 Aug 1995 13:58:54 GMT"
},
{
"version": "v3",
"created": "Thu, 20 Apr 2000 15:00:52 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Grinevich",
"P. G.",
""
],
[
"Novikov",
"S. P.",
""
]
] |
solv-int/9501003 | Fabian Essler | Fabian H.L. Essler (Univ. Bonn) and Vladimir E. Korepin (ITP Stony
Brook) | Dual Field Approach to Correlation Functions in the Heisenberg Xxz Spin
Chain | 19 pages LaTeX, to appear in the proceedings of SMQFT, Los Angeles
1994 | null | null | null | solv-int nlin.SI | null | We study zero temperature correlation functions of the spin-$1\over 2$
Heisenberg XXZ model in the critical regime $-1< \Delta\leq 1$ in a magnetic
field by means of the {\tenit Dual Field Approach}. We show for one particular
example how to derive determinant representations for correlation functions and
how to use these to embed the correlation functions in integrable systems of
integro-difference equations (IDE). These IDE are associated with a
Riemann-Hilbert problem.
| [
{
"version": "v1",
"created": "Wed, 11 Jan 1995 23:10:09 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Essler",
"Fabian H. L.",
"",
"Univ. Bonn"
],
[
"Korepin",
"Vladimir E.",
"",
"ITP Stony\n Brook"
]
] |
solv-int/9501004 | Mark Mineev | Mark B. Mineev-Weinstein | Conservation Laws in Field Dynamics or Why Boundary Motion is Exactly
Integrable? | LaTeX file, 12 pages | null | null | null | solv-int nlin.SI | null | An infinite number of conserved quantities in the field dynamics $\phi_t = L
U(\phi) + \rho$ for a linear Hermitian (or anti-Hermitian) operator $L$, an
arbitrary function $U$ and a given source $\rho$ are presented. These integrals
of motion are the multipole moments of the potential created by $\phi$ in the
far-field. In the singular limit of a bistable scalar field $\phi = \phi_{\pm}$
(i.e. Ising limit) this theory describes a dissipative boundary motion (such as
Stefan or Saffman-Taylor problem that is the continuous limit of the
DLA-fractal growth) and can be exactly integrable. These conserved quantities
are the polynomial conservation laws attributed to the integrability. The
criterion for integrability is the uniqueness of the inverse potential
problem's solution.
| [
{
"version": "v1",
"created": "Wed, 11 Jan 1995 23:32:14 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Mineev-Weinstein",
"Mark B.",
""
]
] |
solv-int/9501005 | Saburo Kakei | Saburo Kakei, Narimasa Sasa and Junkichi Satsuma | Bilinearization of a Generalized Derivative Nonlinear Schr\"odinger
equation | 7 pages, LaTeX file, no figures | J. Phys. Soc. Jpn. 64 (1995) 1519 | 10.1143/JPSJ.64.1519 | null | solv-int nlin.SI | null | A generalized derivative nonlinear Schr\"odinger equation,
\ii q_t + q_{xx} + 2\ii \gamma |q|^2 q_x + 2\ii (\gamma-1)q^2 q^*_x +
(\gamma-1)(\gamma-2)|q|^4 q = 0 ,
is studied by means of Hirota's bilinear formalism. Soliton solutions are
constructed as quotients of Wronski-type determinants. A relationship between
the bilinear structure and gauge transformation is also discussed.
| [
{
"version": "v1",
"created": "Tue, 17 Jan 1995 08:42:01 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Kakei",
"Saburo",
""
],
[
"Sasa",
"Narimasa",
""
],
[
"Satsuma",
"Junkichi",
""
]
] |
solv-int/9501006 | null | P.G.Grinevich & S.P.Novikov | Nonselfintersecting magnetic orbits on the plane. Proof of Principle of
the Overthrowing of the Cycles. | 33 pages, LaTeX. | Transl. of Amer. Math. Soc. series 2 v 170 (1995) 199-206 | null | null | solv-int hep-th nlin.SI | null | Beginning from 1981 one of the present authors (S.Novikov) published a series
of papers, (some of them in collaboration with I.Schmelzer and I.Taimanov)
dedicated to the development of the analog of Morse theory for the closed
1-forms -- multivalued functions and functionals -- on the finite - and
infinite-dimensional manifolds ({\bf Morse-Novikov Theory}).
The notion of ``Multivalued action'' was understood and ``Topological
quantization of the coupling constant'' for them was formulated by Novikov in
1981 as a Corollary from the requirement, that the Feinmann Amplitude should be
one-valued on the space of fields-maps. Very beautiful analog of this theory
appeared also in the late 80-ies in the Symplectic Geometry and Topology, when
the so-called Floer Homology Theory was discovered. A very first topological
idea of this theory, formulated in early 80-ies, was the so-called ``Principle
of the Overthrowing of the Cycles''. It led to the results which were not
proved rigorously until now. Our goal is to prove some of them.
We study the motion of a classical charged particle on the Euclidean plane in
a magnetic field orthogonal to this field. The trajectories of this motion can
be characterized as extremals of the ``Maupertui--Fermat'' functional. We show
that for any smooth everyvhere positive double periodic magnetic field for any
fixed energy there exist at least two different periodic convex extremals, such
that the value of the Maupertui-Fermat functional is positive for them. If all
such extremals are nondegenerate in the sense of Morse in the space of
nonparameterized curves then for any energy there exist at least 4 periodic
convex extremals with the Morse indices (1,2,2,3).
| [
{
"version": "v1",
"created": "Wed, 18 Jan 1995 11:07:58 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Grinevich",
"P. G.",
""
],
[
"Novikov",
"S. P.",
""
]
] |
solv-int/9501007 | Leonid Vitalevich Bogdanov | L.V. Bogdanov (IINS, Landau Institute for Theoretical Physics,
Russia), B.G. Konopelchenko (Dipartimento di Fisica dell'Universit\`a, Lecce,
Italy) | Lattice and q-difference Darboux-Zakharov-Manakov systems via
$\bar{\partial}$-dressing method | 8 pages, LaTeX, to be published in J Phys A, Letters. | null | 10.1088/0305-4470/28/5/005 | null | solv-int math.QA nlin.SI q-alg | null | A general scheme is proposed for introduction of lattice and q-difference
variables to integrable hierarchies in frame of $\bar{\partial}$-dressing
method . Using this scheme, lattice and q-difference Darboux-Zakharov-Manakov
systems of equations are derived. Darboux, B\"acklund and Combescure
transformations and exact solutions for these systems are studied.
| [
{
"version": "v1",
"created": "Sat, 28 Jan 1995 03:53:19 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Bogdanov",
"L. V.",
"",
"IINS, Landau Institute for Theoretical Physics,\n Russia"
],
[
"Konopelchenko",
"B. G.",
"",
"Dipartimento di Fisica dell'Università, Lecce,\n Italy"
]
] |
solv-int/9501008 | null | E. Alfinito, M. Leo, R.A. Leo, M. Palese and G. Soliani | Integrable nonlinear field equations and loop algebra structures | 13 pages, latex, no figures, | Phys. Lett. B352, 314 (1995) | 10.1016/0370-2693(95)00561-X | null | solv-int cond-mat hep-th nlin.SI | null | We apply the (direct and inverse) prolongation method to a couple of
nonlinear Schr{\"o}dinger equations. These are taken as a laboratory field
model for analyzing the existence of a connection between the integrability
property and loop algebras. Exploiting a realization of the Kac-Moody type of
the incomplete prolongation algebra associated with the system under
consideration, we develop a procedure with allows us to generate a new class of
integrable nonlinear field equations containing the original ones as a special
case.
| [
{
"version": "v1",
"created": "Mon, 30 Jan 1995 15:12:44 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Alfinito",
"E.",
""
],
[
"Leo",
"M.",
""
],
[
"Leo",
"R. A.",
""
],
[
"Palese",
"M.",
""
],
[
"Soliani",
"G.",
""
]
] |
solv-int/9501009 | Chris Jarzynski | Christopher Jarzynski | Geometric phase effects for wavepacket revivals | Revtex, 11 pages, no figures. | Phys.Rev.Lett. 74 (1995) 1264 | 10.1103/PhysRevLett.74.1264 | DOE/ER/40561-180-INT94-14-03 | solv-int nlin.SI quant-ph | null | The study of wavepacket revivals is extended to the case of Hamiltonians
which are made time-dependent through the adiabatic cycling of some parameters.
It is shown that the quantal geometric phase (Berry's phase) causes the revived
packet to be displaced along the classical trajectory, by an amount equal to
the classical geometric phase (Hannay's angle), in one degree of freedom. A
physical example illustrating this effect in three degrees of freedom is
mentioned.
| [
{
"version": "v1",
"created": "Thu, 2 Feb 1995 22:23:17 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Jarzynski",
"Christopher",
""
]
] |
solv-int/9502001 | Jarmo Hietarinta | J. Hietarinta, T. Kuusela and B. Malomed | Shock waves in the dissipative Toda lattice | 10 pages in LaTeX, 5 figures available upon reguest | null | 10.1088/0305-4470/28/11/007 | null | solv-int nlin.SI | null | We consider the propagation of a shock wave (SW) in the damped Toda lattice.
The SW is a moving boundary between two semi-infinite lattice domains with
different densities. A steadily moving SW may exist if the damping in the
lattice is represented by an ``inner'' friction, which is a discrete analog of
the second viscosity in hydrodynamics. The problem can be considered
analytically in the continuum approximation, and the analysis produces an
explicit relation between the SW's velocity and the densities of the two
phases. Numerical simulations of the lattice equations of motion demonstrate
that a stable SW establishes if the initial velocity is directed towards the
less dense phase; in the opposite case, the wave gradually spreads out. The
numerically found equilibrium velocity of the SW turns out to be in a very good
agreement with the analytical formula even in a strongly discrete case. If the
initial velocity is essentially different from the one determined by the
densities (but has the correct sign), the velocity does not significantly
alter, but instead the SW adjusts itself to the given velocity by sending
another SW in the opposite direction.
| [
{
"version": "v1",
"created": "Fri, 3 Feb 1995 10:00:30 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Hietarinta",
"J.",
""
],
[
"Kuusela",
"T.",
""
],
[
"Malomed",
"B.",
""
]
] |
solv-int/9502002 | Richard Ward | R. S. Ward | Discrete Toda Field Equations | 7 pages, plainTeX | null | 10.1016/0375-9601(95)00108-F | DTP/95/3; NI94031 | solv-int hep-th nlin.SI | null | There are two-dimensional Toda field equations corresponding to each (finite
or affine) Lie algebra. The question addressed in this note is whether there
exist integrable discrete versions of these. It is shown that for certain
algebras (such as $A_n$, $A_n^{(1)}$ and $B_n$) there do, but some of these
systems are defined on the half-plane rather than the full two-dimensional
lattice.
| [
{
"version": "v1",
"created": "Wed, 8 Feb 1995 14:37:15 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Ward",
"R. S.",
""
]
] |
solv-int/9502003 | David Fairlie | D.B. Fairlie and I.A.B. Strachan | The Hamiltonian structure of the dispersionless Toda hierarchy | 12 pages, latex, no figures | Physica D: Vol 90, Issues 1-2 (1996), 1-8 | 10.1016/0167-2789(95)00229-4 | DTP/95/5 | solv-int nlin.SI | null | The Hamiltonian structure of the two-dimensional dispersionless Toda
hierarchy is studied, this being a particular example of a system of
hydrodynamic type. The polynomial conservation laws for the system turn out,
after a change of variable, to be associated with the axially symmetric
solutions of the 3-dimensional Laplace equation and this enables a generating
function for the Hamiltonian densities to be derived in closed form.
| [
{
"version": "v1",
"created": "Mon, 13 Feb 1995 16:41:01 GMT"
}
] | 2020-12-16T00:00:00 | [
[
"Fairlie",
"D. B.",
""
],
[
"Strachan",
"I. A. B.",
""
]
] |
solv-int/9502004 | Piotr Goldstein | Jan Cie\'sli\'nski (Warsaw University Division in Bia{\l}ystok,
Institute of Physics, Bia{\l}ystok, Poland), Piotr Goldstein (Soltan
Institute for Nuclear Studies, Warsaw, Poland), and Antoni Sym (Warsaw
University, Institute of Theoretical Physics, Warsaw, Poland) | Isothermic surfaces in $\E^3$ as soliton surfaces | Revised version; 13 pages in LaTeX, 1 figure PostScript; to appear in
Physics Letters A | null | 10.1016/0375-9601(95)00504-V | null | solv-int dg-ga math.DG nlin.SI | null | We show that the theory of isothermic surfaces in $\E^3$ -- one of the oldest
branches of differential geometry -- can be reformulated within the modern
theory of completely integrable (soliton) systems. This enables one to study
the geometry of isothermic surfaces in $\E^3$ by means of powerful spectral
methods available in the soliton theory. Also the associated non-linear system
is interesting in itself since it displays some unconventional soliton features
and, physically, could be applied in the theory of infinitesimal deformations
of membranes.
| [
{
"version": "v1",
"created": "Tue, 14 Feb 1995 18:53:01 GMT"
},
{
"version": "v2",
"created": "Thu, 20 Jul 1995 16:40:19 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Cieśliński",
"Jan",
"",
"Warsaw University Division in Białystok,\n Institute of Physics, Białystok, Poland"
],
[
"Goldstein",
"Piotr",
"",
"Soltan\n Institute for Nuclear Studies, Warsaw, Poland"
],
[
"Sym",
"Antoni",
"",
"Warsaw\n University, Institute of Theoretical Physics, Warsaw, Poland"
]
] |
solv-int/9502005 | Benzion Shklyar | B. Shklyar (Dept. of Math., Bar-Ilan Univ.,Ramat Gan, Israel) | On The Observability For Distributed Systems By Means Of Linear
Operations | 20 pages, LaTeX | null | null | bimacs-95 | solv-int nlin.SI | null | An observability problem for linear autonomous distributed systems in the
class of linear operations is considered. A criterion of observability with
respect to terminal state has been proved. A connection with observability with
respect to initial state is discussed.
| [
{
"version": "v1",
"created": "Thu, 16 Feb 1995 18:02:55 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Shklyar",
"B.",
"",
"Dept. of Math., Bar-Ilan Univ.,Ramat Gan, Israel"
]
] |
solv-int/9502006 | Yuji Kodama | Y. Kodama, and K. T-R McLaughlin | Explicit Integration of the Full Symmetric Toda Hierarchy and the
Sorting Property | 13 pages, Latex. | null | 10.1007/BF00400137 | null | solv-int nlin.SI | null | We give an explicit formula for the solution to the initial value problem of
the full symmetric Toda hierarchy. The formula is obtained by the
orthogonalization procedure of Szeg\"{o}, and is also interpreted as a
consequence of the QR factorization method of Symes \cite{symes}. The sorting
property of the dynamics is also proved for the case of a generic symmetric
matrix in the sense described in the text, and generalizations of tridiagonal
formulae are given for the case of matrices with $2M+1$ nonzero diagonals.
| [
{
"version": "v1",
"created": "Wed, 22 Feb 1995 17:49:48 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Kodama",
"Y.",
""
],
[
"McLaughlin",
"K. T-R",
""
]
] |
solv-int/9503001 | Liu Qing-ping | Q.P. Liu | Supersymmetric Harry Dym Type Equations | 4 pages, latex, no figures | null | 10.1088/0305-4470/28/8/004 | CUMT-MATH-95-01 | solv-int nlin.SI | null | A supersymmetric version is proposed for the well known Harry Dym system. A
general class super Lax operator which leads to consistent equations is
considered.
| [
{
"version": "v1",
"created": "Fri, 17 Mar 1995 16:25:25 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Liu",
"Q. P.",
""
]
] |
solv-int/9503002 | Leon Jerome | C. Claude and J. Leon (Physique Mathematique et Theorique, CNRS-URA
768, Universite Montpellier II, 34095 MONTPELLIER FRANCE) | Theory of Pump Depletion and Spike Formation in Stimulated Raman
Scattering | LaTex file, includes two figures in LaTex format, 9 pages | null | 10.1103/PhysRevLett.74.3479 | PM 94-16 | solv-int nlin.PS nlin.SI patt-sol | null | By using the inverse spectral transform, the SRS equations are solved and the
explicit output data is given for arbitrary laser pump and Stokes seed profiles
injected on a vacuum of optical phonons. For long duration laser pulses, this
solution is modified such as to take into account the damping rate of the
optical phonon wave. This model is used to interprete the experiments of Druhl,
Wenzel and Carlsten (Phys. Rev. Lett., (1983) vol. 51, p. 1171), in particular
the creation of a spike of (anomalous) pump radiation. The related nonlinear
Fourier spectrum does not contain discrete eigenvalue, hence this Raman spike
is not a soliton.
| [
{
"version": "v1",
"created": "Fri, 17 Mar 1995 10:41:45 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Claude",
"C.",
"",
"Physique Mathematique et Theorique, CNRS-URA\n 768, Universite Montpellier II, 34095 MONTPELLIER FRANCE"
],
[
"Leon",
"J.",
"",
"Physique Mathematique et Theorique, CNRS-URA\n 768, Universite Montpellier II, 34095 MONTPELLIER FRANCE"
]
] |
solv-int/9503003 | Denis V. Juriev | Denis V.Juriev | On the dynamics of noncanonically coupled oscillators and its hidden
superstructure | revised version -- refs are updated | null | null | ESI-167 | solv-int nlin.SI | null | The classical and quantum dynamics of the noncanonically coupled oscillators
is considered. It is shown that though the classical dynamics is well--defined
for both harmonic and anharmonic oscillators, the quantum one is well--defined
in the harmonic case, admits a hidden (super)Hamiltonian formulation, and thus,
preserves the initial operator relations, whereas a na\"\i ve quantization of
the anharmonic case meets with principal difficulties.
| [
{
"version": "v1",
"created": "Sat, 25 Mar 1995 10:31:03 GMT"
},
{
"version": "v2",
"created": "Sun, 6 Aug 1995 05:50:07 GMT"
},
{
"version": "v3",
"created": "Thu, 4 Apr 1996 04:59:30 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Juriev",
"Denis V.",
""
]
] |
solv-int/9504001 | Evgenii Sklyanin | E.K. Sklyanin | Separation of Variables. New Trends. | 33 pages, harvmac, no figures | Prog.Theor.Phys.Suppl.118:35-60,1995 | 10.1143/PTPS.118.35 | UTMS 95-9 | solv-int nlin.SI | null | The review is based on the author's papers since 1985 in which a new approach
to the separation of variables (\SoV) has being developed. It is argued that
\SoV, understood generally enough, could be the most universal tool to solve
integrable models of the classical and quantum mechanics. It is shown that the
standard construction of the action-angle variables from the poles of the
Baker-Akhiezer function can be interpreted as a variant of \SoV, and moreover,
for many particular models it has a direct quantum counterpart. The list of the
models discussed includes XXX and XYZ magnets, Gaudin model, Nonlinear
Schr\"odinger equation, $SL(3)$-invariant magnetic chain. New results for the
3-particle quantum Calogero-Moser system are reported.
| [
{
"version": "v1",
"created": "Tue, 4 Apr 1995 09:34:27 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Sklyanin",
"E. K.",
""
]
] |
solv-int/9504002 | Costas Efthimiou | S. A. APIKYAN (Yerevan Physics Institute) and C. J. EFTHIMIOU (Cornell
University) | $V_{(1,1)}^{(t)}$-PERTURBED MODELS OF CFT AND THEIR QUANTUM GROUP
SYMMETRY | 16 pages, LaTeX file, AMS fonts | Phys.Lett. B359 (1995) 313-320 | 10.1016/0370-2693(95)01075-2 | Cornell preprint CLNS 95/1330 | solv-int hep-th nlin.SI | null | We propose a new massive integrable model in quantum field theory. This model
is obtained as a perturbed model of the minimal conformal field theories on the
hyper-elliptic surfaces by a particular relavant operator $V_{(1,1)}^{(t)}$.
The non-local conserved charges of the model and their $q$-deformed algebra are
also constructed explicitly.
| [
{
"version": "v1",
"created": "Wed, 5 Apr 1995 23:57:10 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"APIKYAN",
"S. A.",
"",
"Yerevan Physics Institute"
],
[
"EFTHIMIOU",
"C. J.",
"",
"Cornell\n University"
]
] |
solv-int/9504003 | Liu Qing-ping | Q.P. Liu | Painlev\'{e} Analysis and Exact Solutions of a Modified Boussinesq
Equation | 7 pages, LaTeX file | null | null | CUMT-Math-9504 | solv-int nlin.SI | null | We consider a modified Boussinesq type equation. The Painlev\'{e} test of the
WTC method is performed for this equation and it shows that the equation has
weak Painlev\'{e} property. Some exact solutions are constructed.
| [
{
"version": "v1",
"created": "Thu, 27 Apr 1995 15:44:46 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Liu",
"Q. P.",
""
]
] |
solv-int/9505001 | Denis V. Juriev | Denis V. Juriev | Topics in nonhamiltonian (magnetic-type) interaction of classical
hamiltonian dynamical systems. I | AMSTEX 9 pages, a slightly revised version | Russian J.Math.Phys.3(4)(1995) | null | null | solv-int nlin.SI | null | A convenient algebraic structure to describe some forms of dynamics of two
hamiltonian systems with nonpotential (magnetic--type) interaction is
considered. An algebraic mechanism of generation of such dynamics is explored
on simple "toy" examples and models. Nonpotential chains and their continuum
limits are also considered. Examples of hybrid couplings with both potential
and nonpotential (magnetic--type) interactions are discussed.
| [
{
"version": "v1",
"created": "Fri, 5 May 1995 12:46:52 GMT"
},
{
"version": "v2",
"created": "Sun, 6 Aug 1995 00:55:33 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Juriev",
"Denis V.",
""
]
] |
solv-int/9505002 | Andrzej Maciejewski | Andrzej J.~Maciejewski (Institute of Astronomy, N. Copernicus
University, Chopina 12-18, 87-100 Toru\'n, Poland), Jean-Marie Strelcyn
(D\'epartement de Math\'ematiques, Universit\'e de Rouen,76821 Mont Saint
Aignan Cedex, France, URA CNRS 1378) | On the algebraic non-integrability of the Halphen system | 10 pages, AMSLaTeX, to appear in Physics Letters A | null | null | null | solv-int nlin.SI | null | It is proved that the Halphen system of ordinary differential equations has
no non-trivial rational first integrals.
| [
{
"version": "v1",
"created": "Fri, 12 May 1995 16:17:23 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"~Maciejewski",
"Andrzej J.",
"",
"Institute of Astronomy, N. Copernicus\n University, Chopina 12-18, 87-100 Toruń, Poland"
],
[
"Strelcyn",
"Jean-Marie",
"",
"Département de Mathématiques, Université de Rouen,76821 Mont Saint\n Aignan Cedex, France, URA CNRS 1378"
]
] |
solv-int/9505003 | Adler | V.E. Adler and I.T. Habibullin (Ufa Institute of Mathematics, Russian
Academy of Sciences, Chernyshevsky str. 112, 450000 Ufa, Russia) | Integrable boundary conditions for the Toda lattice | null | null | 10.1088/0305-4470/28/23/021 | null | solv-int nlin.SI | null | The problem of construction of the boundary conditions for the Toda lattice
compatible with its higher symmetries is considered. It is demonstrated that
this problem is reduced to finding of the differential constraints consistent
with the ZS-AKNS hierarchy. A method of their construction is offered based on
the B\"acklund transformations. It is shown that the generalized Toda lattices
corresponding to the non-exceptional Lie algebras of finite growth can be
obtained by imposing one of the four simplest integrable boundary conditions on
the both ends of the lattice. This fact allows, in particular, to solve the
problem of reduction of the series $A$ Toda lattices into the series $D$ ones.
Deformations of the found boundary conditions are presented which leads to the
Painlev\'e type equations.
Key words: Toda lattice, boundary conditions, integrability, B\"acklund
transformation, Lie algebras, Painlev\'e equations
| [
{
"version": "v1",
"created": "Wed, 17 May 1995 03:00:01 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Adler",
"V. E.",
"",
"Ufa Institute of Mathematics, Russian\n Academy of Sciences, Chernyshevsky str. 112, 450000 Ufa, Russia"
],
[
"Habibullin",
"I. T.",
"",
"Ufa Institute of Mathematics, Russian\n Academy of Sciences, Chernyshevsky str. 112, 450000 Ufa, Russia"
]
] |
solv-int/9505004 | Yuji Kodama | Yuji Kodama, and Jian Ye | Toda Hierarchy with Indefinite Metric | 26 pages, LaTeX | null | 10.1016/0167-2789(95)00269-3 | null | solv-int hep-th nlin.SI | null | We consider a generalization of the full symmetric Toda hierarchy where the
matrix $\tilde {L}$ of the Lax pair is given by $\tilde {L}=LS$, with a full
symmetric matrix $L$ and a nondegenerate diagonal matrix $S$. The key feature
of the hierarchy is that the inverse scattering data includes a class of
noncompact groups of matrices, such as $O(p,q)$. We give an explicit formula
for the solution to the initial value problem of this hierarchy. The formula is
obtained by generalizing the orthogonalization procedure of Szeg\"{o}, or the
QR factorization method of Symes. The behaviors of the solutions are also
studied. Generically, there are two types of solutions, having either sorting
property or blowing up to infinity in finite time. The $\tau$-function
structure for the tridiagonal hierarchy is also studied.
| [
{
"version": "v1",
"created": "Fri, 19 May 1995 15:17:21 GMT"
}
] | 2015-06-26T00:00:00 | [
[
"Kodama",
"Yuji",
""
],
[
"Ye",
"Jian",
""
]
] |
solv-int/9505005 | Latypov A. M. | Azat M.Latypov (Fluid Dynamics Research Institute and Department of
Mathematics and Statistics, University of Windsor, CANADA) | Approximate Lie Group Analysis of a Model Advection Equation on an
Unstructured Grid | 8 pages, LaTeX | null | null | null | solv-int comp-gas nlin.CG nlin.SI | null | A technique of ``approximate group analysis'' recently developed by Baikov,
Gazizov and Ibragimov is applied to a differential approximation (otherwise
referred to as an equivalent differential equation) corresponding to the finite
difference approximation of a nonlinear advection equation on unstructured
grid. We determine which groups from the infinite variety of groups admitted by
a nonlinear advection equation ``survive'' the discretization. The situations
arising for different choices of an arbitrary function (local speed of
propagation) are also studied.
| [
{
"version": "v1",
"created": "Tue, 30 May 1995 07:14:16 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Latypov",
"Azat M.",
"",
"Fluid Dynamics Research Institute and Department of\n Mathematics and Statistics, University of Windsor, CANADA"
]
] |
solv-int/9505006 | null | R.Z.Zhdanov | Conditional Lie-B\"acklund symmetry and reduction of evolution
equations. | 12 pages, latex, needs amssymb., to appear in the "Journal of Physics
A: Mathematical and General" (1995) | null | 10.1088/0305-4470/28/13/027 | null | solv-int nlin.SI | null | We suggest a generalization of the notion of invariance of a given partial
differential equation with respect to Lie-B\"acklund vector field. Such
generalization proves to be effective and enables us to construct principally
new Ans\"atze reducing evolution-type equations to several ordinary
differential equations. In the framework of the said generalization we obtain
principally new reductions of a number of nonlinear heat conductivity equations
$u_t=u_{xx}+F(u,u_x)$ with poor Lie symmetry and obtain their exact solutions.
It is shown that these solutions can not be constructed by means of the
symmetry reduction procedure.
| [
{
"version": "v1",
"created": "Wed, 31 May 1995 06:50:33 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Zhdanov",
"R. Z.",
""
]
] |
solv-int/9506001 | Hikami Kazuhiro | Kazuhiro Hikami | Separation of Variables in BC-type Gaudin Magnet | 11 pages, macros from ftp.ioppublishing.com | null | 10.1088/0305-4470/28/14/023 | null | solv-int nlin.SI | null | The integrable system is introduced based on the Poisson $ rs $-matrix
structure. This is a generalization of the Gaudin magnet, and in SL(2) case
isomorphic to the generalized Neumann model. The separation of variables is
discussed for both classical and quantum case.
| [
{
"version": "v1",
"created": "Wed, 7 Jun 1995 11:29:16 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Hikami",
"Kazuhiro",
""
]
] |
solv-int/9506002 | Daniel Finley | J. D. Finley, III, John K. McIver (University of New Mexico) | Infinite-Dimensional Estabrook-Wahlquist Prolongations for the
sine-Gordon Equation | 46 pages, plain TeX, no figures, to be published in J. Math. Phys. | null | 10.1063/1.531348 | null | solv-int nlin.SI | null | We are looking for the universal covering algebra for all symmetries of a
given pde, using the sine-Gordon equation as a typical example for a
non-evolution equation. For non-evolution equations, Estabrook-Wahlquist
prolongation structures for non-local symmetries depend on the choice of a
specific sub-ideal, of the contact module, to define the pde. For each
inequivalent such choice we determine the most general solution of the
prolongation equations, as sub-algebras of the (infinite-dimensional) algebra
of all vector fields over the space of non-local variables associated with the
pde, in the style of Vinogradov covering spaces. We show explicitly how
previously-known prolongation structures, known to lie within the Kac-Moody
algebra, $A_1^{(1)}$, are special cases of these general solutions, although we
are unable to identify the most general solutions with previously-studied
algebras. We show the existence of gauge transformations between prolongation
structures, viewed as determining connections over the solution space, and use
these to relate (otherwise) distinct algebras. Faithful realizations of the
universal algebra allow integral representations of the prolongation structure,
opening up interesting connections with algebras of Toeplitz operators over
Banach spaces, an area that has only begun to be explored.
| [
{
"version": "v1",
"created": "Fri, 9 Jun 1995 19:27:54 GMT"
}
] | 2012-08-27T00:00:00 | [
[
"Finley",
"J. D.",
"",
"University of New Mexico"
],
[
"III",
"",
"",
"University of New Mexico"
],
[
"McIver",
"John K.",
"",
"University of New Mexico"
]
] |
solv-int/9506003 | Igor Germanovich Korepanov | I.G. Korepanov | Algebraic integrable dynamical systems, 2+1-dimensional models in wholly
discrete space-time, and inhomogeneous models in 2-dimensional statistical
physics | 1) Normally, this must be LaTeXed 3 times! (I beg your pardon) 2)
your TeX system must include the \special{em: ...} commands to get the
pictures properly, 3) even if it does, one figure is missing--you will see an
empty space of height about 8 cm, with a caption below it. Please contact the
author | null | null | null | solv-int nlin.SI | null | This paper is devoted to constructing and studying exactly solvable dynamical
systems in discrete time obtained from some algebraic operations on matrices,
to reductions of such systems leading to classical field theory models in
2+1-dimensional wholly discrete space-time, and to connection between those
field theories and inhomogoneous models in 2-dimensional statistical physics.
| [
{
"version": "v1",
"created": "Sat, 1 Jul 1995 12:36:58 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Korepanov",
"I. G.",
""
]
] |
solv-int/9506004 | Adam Doliwa | Adam Doliwa (Institute of Theoretical Physics, Warsaw University) | Holomorphic Curves and Toda Systems | 14 pages, LaTeX (minor spelling changes) | Lett. Math. Phys. 39 (1997) 21 | 10.1007/s11005-997-1032-7 | IFT 7/95 | solv-int alg-geom dg-ga math.AG math.DG nlin.SI | null | Geometry of holomorphic curves from point of view of open Toda systems is
discussed. Parametrization of curves related this way to non-exceptional simple
Lie algebras is given. This gives rise to explicit formulas for minimal
surfaces in real, complex and quaternionic projective spaces or complex
quadrics. The paper generalizes the well known connection between minimal
surfaces in $\EE^{3}$, their Weierstrass representation in terms of holomorphic
functions and the general solution to the Liouville equation.
| [
{
"version": "v1",
"created": "Mon, 3 Jul 1995 15:37:43 GMT"
},
{
"version": "v2",
"created": "Tue, 4 Jul 1995 12:38:09 GMT"
}
] | 2015-06-26T00:00:00 | [
[
"Doliwa",
"Adam",
"",
"Institute of Theoretical Physics, Warsaw University"
]
] |
solv-int/9506005 | Yuji Kodama | Yuji Kodama and Jian Ye | Iso-spectral deformations of general matrix and their reductions on Lie
algebras | 25 pages, AMSLaTex | null | 10.1007/BF02108824 | null | solv-int hep-th nlin.SI | null | We study an iso-spectral deformation of general matrix which is a natural
generalization of the Toda lattice equation. We prove the integrability of the
deformation, and give an explicit formula for the solution to the initial value
problem. The formula is obtained by generalizing the orthogonalization
procedure of Szeg\"{o}. Based on the root spaces for simple Lie algebras, we
consider several reductions of the hierarchy. These include not only the
integrable systems studied by Bogoyavlensky and Kostant, but also their
generalizations which were not known to be integrable before. The behaviors of
the solutions are also studied. Generically, there are two types of solutions,
having either sorting property or blowing up to infinity in finite time.
| [
{
"version": "v1",
"created": "Mon, 3 Jul 1995 18:15:34 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Kodama",
"Yuji",
""
],
[
"Ye",
"Jian",
""
]
] |
solv-int/9506006 | Craig A. Tracy | Craig A. Tracy (Univ. of California, Davis), Harold Widom (Univ. of
California, Santa Cruz) | Fredholm determinants and the mKdV/sinh-Gordon hierarchies | 11 pages, LaTeX file, no figures | Commun. Math. Phys 179 (1996) 1--9 | 10.1007/BF02103713 | null | solv-int hep-th math-ph math.MP nlin.SI | null | For a particular class of integral operators $K$ we show that the quantity
\[\ph:=\log \det (I+K)-\log \det (I-K)\] satisfies both the integrated mKdV
hierarchy and the sinh-Gordon hierarchy. This proves a conjecture of
Zamolodchikov.
| [
{
"version": "v1",
"created": "Fri, 7 Jul 1995 01:17:41 GMT"
}
] | 2009-07-11T00:00:00 | [
[
"Tracy",
"Craig A.",
"",
"Univ. of California, Davis"
],
[
"Widom",
"Harold",
"",
"Univ. of\n California, Santa Cruz"
]
] |
solv-int/9507001 | Costas Efthimiou | Costas J. Efthimiou (Cornell University) and Samwel A. Apikyan
(Yerevan Physics Insitute) | Integrable Models on Hyper-Elliptic Surfaces | uuencoded Z-compressed postscript file | null | null | Cornell Preprint CLNS 95/1342 | solv-int hep-th nlin.SI | null | We present an elementary introduction to the construction of integrable
models on hyper-elliptic surfaces for non specialists; also, we present some of
the details of the paper `solv-int/9504002' for the more interested readers.
(Based on a talk given at the MRST 95 meeting by C. E.)
| [
{
"version": "v1",
"created": "Wed, 12 Jul 1995 23:04:33 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Efthimiou",
"Costas J.",
"",
"Cornell University"
],
[
"Apikyan",
"Samwel A.",
"",
"Yerevan Physics Insitute"
]
] |
solv-int/9507002 | Jan Felipe van Diejen | J. F. van Diejen | Multivariable continuous Hahn and Wilson polynomials related to
integrable difference systems | 5 pages, REVTEX, to appear in J. Phys. A: Math. Gen | J. Phys. A: Math. Gen. 28 (1995) L369-74 | 10.1088/0305-4470/28/13/003 | null | solv-int nlin.SI | null | Multivariable generalizations of the continuous Hahn and Wilson polynomials
are introduced as eigenfunctions of rational Ruijsenaars type difference
systems with an external field.
| [
{
"version": "v1",
"created": "Wed, 19 Jul 1995 10:00:54 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"van Diejen",
"J. F.",
""
]
] |
solv-int/9507003 | null | Renat Z. Zhdanov, Ihor V. Revenko and Wilhelm I. Fushchych | On the new approach to variable separation in the time-dependent
Schr\"odinger equation with two space dimensions | 21 pages, latex, to appear in the "Journal of Mathematical Physics"
(1995) | null | 10.1063/1.531274 | null | solv-int hep-ph nlin.SI | null | We suggest an effective approach to separation of variables in the
Schr\"odinger equation with two space variables. Using it we classify
inequivalent potentials $V(x_1,x_2)$ such that the corresponding Schr\" odinger
equations admit separation of variables. Besides that, we carry out separation
of variables in the Schr\" odinger equation with the anisotropic harmonic
oscillator potential $V=k_1x_1^2+k_2x_2^2$ and obtain a complete list of
coordinate systems providing its separability. Most of these coordinate systems
depend essentially on the form of the potential and do not provide separation
of variables in the free Schr\" odinger equation ($V=0$).
| [
{
"version": "v1",
"created": "Thu, 20 Jul 1995 07:46:02 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Zhdanov",
"Renat Z.",
""
],
[
"Revenko",
"Ihor V.",
""
],
[
"Fushchych",
"Wilhelm I.",
""
]
] |
solv-int/9507004 | G. Tondo | G. Tondo (Dipartimento di Scienze Matematiche, Universita degli Studi
di Trieste) | On the integrability of stationary and restricted flows of the KdV
hierarchy. | 25 pages, AMS-LATEX 2.09, no figures, to be published in J. Phys. A:
Math. Gen.. | null | 10.1088/0305-4470/28/17/034 | null | solv-int nlin.SI | null | A bi--Hamiltonian formulation for stationary flows of the KdV hierarchy is
derived in an extended phase space. A map between stationary flows and
restricted flows is constructed: in a case it connects an integrable
Henon--Heiles system and the Garnier system. Moreover a new integrability
scheme for Hamiltonian systems is proposed, holding in the standard phase
space.
| [
{
"version": "v1",
"created": "Sat, 22 Jul 1995 14:26:49 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Tondo",
"G.",
"",
"Dipartimento di Scienze Matematiche, Universita degli Studi\n di Trieste"
]
] |
solv-int/9507005 | Nagesha N. Rao | N.N. Rao (Theoretical Physics Division, Physical Research Laboratory,
Navrangpura, Ahmedabad-380009, India) | Henon-Heiles Hamiltonian for Coupled Upper-Hybrid and Magnetoacoutic
Waves in Magnetized Plasmas | 11 pages; Latex file, Two figures upon request submitted to the
Journal, appeared in Phys. Letts., A202, 383 (1995) | null | 10.1016/0375-9601(95)00361-6 | PRL-TH/95-5; | solv-int nlin.SI | null | We show that the coupled mode equations for the stationary propagation of
upper--hybrid and magnetoacoustic waves in magnetized electron--ion plasmas
with negative group dispersion can be exactly derived from the generalized
\Henon--Heiles Hamiltonian. The parameter regimes for the integrable cases of
the coupled mode equations have been explicitly obtained. For positive group
dispersion of the upper--hybrid waves, the relevant governing equations lead to
a novel Hamiltonian where the kinetic energy is not positive definite.
| [
{
"version": "v1",
"created": "Mon, 24 Jul 1995 06:03:19 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Rao",
"N. N.",
"",
"Theoretical Physics Division, Physical Research Laboratory,\n Navrangpura, Ahmedabad-380009, India"
]
] |
solv-int/9507006 | null | A. Zujewski | Hamiltonian Structures on Coadjoint Orbits of Semidirect Product of
$G=Diff_+(S^{1})$ and $C^{\infty}(S^1, {\bf R})$ | 17 pages, LaTeX | null | null | null | solv-int hep-th nlin.SI | null | We consider the semidirect product of diffeomorphisms of the circle
$D={Diff}_+(S^1)$ and $C^{\infty}(S^{1}, {\bf R})$ functions, classify its
coadjoint orbits and prove the integrability of hamiltonian (Generalized
Dispersive Water Waves (DWW) and KdV-type) systems related to corresponding Lie
algebra centrally extended by Kac-Moody, Virasoro and semidirect product
cocycles with arbitrary coefficients.
| [
{
"version": "v1",
"created": "Wed, 2 Aug 1995 12:20:24 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Zujewski",
"A.",
""
]
] |
solv-int/9508001 | Troy Shinbrot | Troy Shinbrot (Rutgers University, Piscataway, NJ) | Integer spin particles necessarily produce half-integer angular momentum
in a simple complex and periodic Hamiltonian | 9 pgs, 2 figures | null | null | null | solv-int nlin.SI | null | Exact wave functions are is derived from an azimuthally periodic a
self-consistent quantum Hamiltonian in 2+1 dimensions using both the
Klein-Gordon and the Schroedinger equations. It isWe shown that, curiously, for
both relativistic and non-relativistic equations, integer spin wave equations
necessarily produce half-integer angular momentum in this potential. We find
additionally that the higher energy, relativistic, solutions require an
asymptotically free potential, while the lower energy, Schroedinger, solutions
can exist in a potential that grows linearly with r. These are purely
mathematical results, however we speculate on possible physical
interpretations.
| [
{
"version": "v1",
"created": "Thu, 10 Aug 1995 17:24:03 GMT"
},
{
"version": "v2",
"created": "Wed, 9 Aug 2006 19:58:45 GMT"
}
] | 2009-09-25T00:00:00 | [
[
"Shinbrot",
"Troy",
"",
"Rutgers University, Piscataway, NJ"
]
] |
solv-int/9508002 | Evgenii Sklyanin | V.B. Kuznetsov (University of Amsterdam) and E.K.Sklyanin (University
of Tokyo) | Separation of variables in the $A_2$ type Jack polynomials | 17 pages, LATEX, macros included, no figures | Various aspects of hypergeometric functions (Japanese) (Kyoto,
1994). Surikaisekikenkyusho Kokyuroku No. 919 (1995), 27-43 | null | UTMS 95-10; UAMS 95-06 | solv-int math.QA nlin.SI q-alg | null | An integral operator $M$ is constructed performing a separation of variables
for the 3-particle quantum Calogero-Sutherland (CS) model. Under the action of
$M$ the CS eigenfunctions (Jack polynomials for the root system $A_2$) are
transformed to the factorized form $\phi(y_1)\phi(y_2)$, where $\phi(y)$ is a
trigonometric polynomial of one variable expressed in terms of the ${}_3F_2$
hypergeometric series. The inversion of $M$ produces a new integral
representation for the $A_2$ Jack polynomials.
| [
{
"version": "v1",
"created": "Mon, 21 Aug 1995 10:14:18 GMT"
}
] | 2015-11-13T00:00:00 | [
[
"Kuznetsov",
"V. B.",
"",
"University of Amsterdam"
],
[
"Sklyanin",
"E. K.",
"",
"University\n of Tokyo"
]
] |
solv-int/9508003 | Robert Conte | Micheline Musette (Vrije Universiteit Brussel) and Robert Conte (CEA
Saclay) | Non-Fuchsian extension to the Painlev\'e test | 15 pages, no figure, Latex, to appear in Physics Letters A | null | 10.1016/0375-9601(95)00602-Y | SPEC 94/118 | solv-int nlin.SI | null | We consider meromorphic particular solutions of nonlinear ordinary
differential equations and perform a perturbation {\it \`a la} Poincar\'e
making their linearized equation non-Fuchsian at the movable pole and Fuchsian
at infinity. When the nonlinear equation possesses movable logarithms, they are
detected sooner than with the perturbative (Fuchsian) Painlev\'e test.
| [
{
"version": "v1",
"created": "Mon, 28 Aug 1995 16:01:37 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Musette",
"Micheline",
"",
"Vrije Universiteit Brussel"
],
[
"Conte",
"Robert",
"",
"CEA\n Saclay"
]
] |
solv-int/9508004 | Tetsu Yajima | Tetsu Yajima and Katsuhiro Nishinari | Numerical Studies of Localized Structures on an Uneven Bottom in Two
Dimensions | 14 pages, RevTeX, 7 figures available upon request | null | null | null | solv-int nlin.SI | null | The Davey-Stewartson (DS) equations with a perturbation term are presented by
taking a fluid system as an example on an uneven bottom. Stability of dromions,
solutions of the DS equations with localized structures, against the
perturbation is investigated numerically. Dromions decay exponentially under an
effect of the perturbation, while they travel stably after the effect
disappears. The decay ratio of dromions is found to have relation to velocities
of dromions. The important role played by the mean flow, which acts as an
external force to the system, is discussed. These results show that dromions
are quite stable as a localized structure in two dimensions, and they are
expected to observed in various physical systems such as fluid or plasma
systems.
| [
{
"version": "v1",
"created": "Wed, 30 Aug 1995 07:29:25 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Yajima",
"Tetsu",
""
],
[
"Nishinari",
"Katsuhiro",
""
]
] |
solv-int/9508005 | Ismagil Habibullin | I.T. Habibullin | Symmetry approach in boundary value problems | 7 pages, LaTeX | null | 10.2991/jnmp.1996.3.1-2.16 | null | solv-int nlin.SI | null | The problem of construction of the boundary conditions for nonlinear
equations is considered compatible with their higher symmetries. Boundary
conditions for the sine-Gordon, Jiber-Shabat and KdV equations are discussed.
New examples are found for the Jiber-Shabat equation.
| [
{
"version": "v1",
"created": "Thu, 31 Aug 1995 07:07:35 GMT"
},
{
"version": "v2",
"created": "Wed, 6 Sep 1995 02:04:35 GMT"
}
] | 2015-06-26T00:00:00 | [
[
"Habibullin",
"I. T.",
""
]
] |
solv-int/9509001 | Vadim B. Kuznetsov | Vadim B. Kuznetsov | Hidden symmetry of the quantum Calogero-Moser system | 16 pages, latex, no figures | Phys.Lett.A218(1996) 212-222 | 10.1016/0375-9601(96)00421-5 | null | solv-int hep-th math.QA nlin.SI q-alg | null | Hidden symmetry of the quantum Calogero-Moser system with the inverse-square
potential is explicitly demonstrated in algebraic sense. We find the underlying
algebra explaining the super-integrability phenomenon for this system.
Applications to related multi-variable Bessel functions are also discussed.
| [
{
"version": "v1",
"created": "Mon, 4 Sep 1995 12:23:57 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Kuznetsov",
"Vadim B.",
""
]
] |
solv-int/9509002 | 1081 | J. F. van Diejen | The relativistic Calogero model in an external field | 10 pages, LaTeX, Submitted to the Proceedings of the 4th Wigner
Symposium, August 5-11, 1995 Guadalajara, Mexico. Third section corrected | null | null | null | solv-int hep-th nlin.SI | null | Recent results are surveyed regarding the spectrum and eigenfunctions of the
inverse square Calogero model with harmonic confinement and its relativistic
analogue.
| [
{
"version": "v1",
"created": "Thu, 7 Sep 1995 01:18:25 GMT"
},
{
"version": "v2",
"created": "Wed, 13 Sep 1995 04:56:24 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"van Diejen",
"J. F.",
""
]
] |
solv-int/9509003 | Craig A. Tracy | Craig A. Tracy (Univ. of California, Davis), Harold Widom (Univ. of
California, Santa Cruz) | Proofs of Two Conjectures Related to the Thermodynamic Bethe Ansatz | 16 pages, LaTeX file, no figures. Revision has minor changes | Commun.Math.Phys. 179 (1996) 667-680 | 10.1007/BF02100102 | null | solv-int hep-th math-ph math.MP nlin.SI | null | We prove that the solution to a pair of nonlinear integral equations arising
in the thermodynamic Bethe Ansatz can be expressed in terms of the resolvent
kernel of the linear integral operator with kernel
exp(-u(theta)-u(theta'))/cosh[(1/2)(theta-theta')]
| [
{
"version": "v1",
"created": "Sat, 9 Sep 1995 00:44:13 GMT"
},
{
"version": "v2",
"created": "Sat, 9 Sep 1995 17:12:41 GMT"
},
{
"version": "v3",
"created": "Tue, 12 Sep 1995 20:44:27 GMT"
}
] | 2009-07-11T00:00:00 | [
[
"Tracy",
"Craig A.",
"",
"Univ. of California, Davis"
],
[
"Widom",
"Harold",
"",
"Univ. of\n California, Santa Cruz"
]
] |
solv-int/9509004 | Pgg | P.G.Grinevich (Landau Institute for Theoretical Physics, Moscow,
Russia) | Nonisospectral symmetries of the KdV equation and the corresponding
symmetries of the Whitham equations | null | null | null | null | solv-int nlin.SI | null | In our paper we construct a new infinite family of symmetries of the Whitham
equations (averaged Korteveg-de-Vries equation). In contrast with the ordinary
hydrodynamic-type flows these symmetries are nonhomogeneous (i.e. they act
nontrivially at the constant solutions), are nonlocal, explicitly depend upon
space and time coordinates and form a noncommutative algebra, isomorphic to the
algebra of the polynomial vector fields in the complex plane (Virasoro algebra
with the zero central charge).
| [
{
"version": "v1",
"created": "Wed, 13 Sep 1995 10:18:25 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Grinevich",
"P. G.",
"",
"Landau Institute for Theoretical Physics, Moscow,\n Russia"
]
] |
solv-int/9509005 | Jarmo Hietarinta | Yunbo Zeng and Jarmo Hietarinta | Classical Poisson structures and r-matrices from constrained flows | 16 pages in LaTeX | null | 10.1088/0305-4470/29/16/038 | null | solv-int math.QA nlin.SI q-alg | null | We construct the classical Poisson structure and $r$-matrix for some finite
dimensional integrable Hamiltonian systems obtained by constraining the flows
of soliton equations in a certain way. This approach allows one to produce new
kinds of classical, dynamical Yang-Baxter structures. To illustrate the method
we present the $r$-matrices associated with the constrained flows of the
Kaup-Newell, KdV, AKNS, WKI and TG hierarchies, all generated by a
2-dimensional eigenvalue problem. Some of the obtained $r$-matrices depend only
on the spectral parameters, but others depend also on the dynamical variables.
For consistency they have to obey a classical Yang-Baxter-type equation,
possibly with dynamical extra terms.
| [
{
"version": "v1",
"created": "Thu, 14 Sep 1995 08:49:51 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Zeng",
"Yunbo",
""
],
[
"Hietarinta",
"Jarmo",
""
]
] |
solv-int/9509006 | Sergei Ya. Startsev | S. Ya. Startsev | Differential substitutions and symmetries of hyperbolic equations | 8 pages, AmSTeX | null | null | null | solv-int nlin.PS nlin.SI patt-sol | null | There are considered differential substitutions of the form $v=P(x,u,u_{x})$
for which there exists a differential operator $H=\sum^{k}_{i=0} \alpha_{i}
D^{i}_{x}$ such that the differential substitution maps the equation
$u_{t}=H[s(x,P,D_{x}(P),...,D^{k}_{x}(P))]$ into an evolution equation for any
function $s$ and any nonnegative integer $k$. All differential substitutions of
the form $v=P(x,u,u_{x})$ known to the author have this property. For example,
the well-known Miura transformation $v=u_{x}-u^{2}$ maps any equation of the
form $$u_{t}=(D^{2}_{x}+2uD_{x}+2u_{x})
[s(x,u_{x}-u^{2},D_{x}(u_{x}-u^{2}),...,D^{k}_{x}(u_{x}-u^{2}))]$$ into the
equation $$v_{t}=(D^{3}_{x}+4vD_{x}+2v_{x})[s(x,v,{{\partial v}\over{\partial x
}},...,{{\partial^{k} v}\over{\partial x^{k}}})].$$ The complete classification
of such differential substitutions is given. An infinite set of the pairwise
nonequivalent differential substitutions with the property mentioned above is
constructed. Moreover, a general result about symmetries and invariant
functions of hyperbolic equations is obtained.
| [
{
"version": "v1",
"created": "Fri, 15 Sep 1995 04:11:50 GMT"
},
{
"version": "v2",
"created": "Mon, 25 Sep 1995 06:51:48 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Startsev",
"S. Ya.",
""
]
] |
solv-int/9509007 | Craig A. Tracy | Craig A. Tracy (Univ. of California, Davis), Harold Widom (Univ. of
California, Santa Cruz) | On Orthogonal and Symplectic Matrix Ensembles | 34 pages. LaTeX file with one figure. To appear in Commun. Math.
Physics | Commun.Math.Phys.177:727-754,1996 | 10.1007/BF02099545 | null | solv-int hep-th math-ph math.MP nlin.SI | null | The focus of this paper is on the probability, $E_\beta(0;J)$, that a set $J$
consisting of a finite union of intervals contains no eigenvalues for the
finite $N$ Gaussian Orthogonal ($\beta=1$) and Gaussian Symplectic ($\beta=4$)
Ensembles and their respective scaling limits both in the bulk and at the edge
of the spectrum. We show how these probabilities can be expressed in terms of
quantities arising in the corresponding unitary ($\beta=2$) ensembles. Our most
explicit new results concern the distribution of the largest eigenvalue in each
of these ensembles. In the edge scaling limit we show that these largest
eigenvalue distributions are given in terms of a particular Painlev\'e II
function.
| [
{
"version": "v1",
"created": "Sun, 17 Sep 1995 16:59:47 GMT"
}
] | 2014-11-18T00:00:00 | [
[
"Tracy",
"Craig A.",
"",
"Univ. of California, Davis"
],
[
"Widom",
"Harold",
"",
"Univ. of\n California, Santa Cruz"
]
] |
solv-int/9509008 | null | J.A. Mulvey (University of Durham) | BiHamiltonian Formulations of the Bateman Equation | 10 pages, LaTeX article, to appear in Phys. Lett. A | null | 10.1016/0375-9601(95)00709-C | DTP/95/51 | solv-int hep-th nlin.SI | null | We discuss a class of evolution equations equivalent to the simplest
Universal Field Equation, the so--called Bateman equation, and show that all of
them possess (at least) biHamiltonian structure. The first few conserved
charges are calculated.
| [
{
"version": "v1",
"created": "Thu, 21 Sep 1995 13:44:23 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Mulvey",
"J. A.",
"",
"University of Durham"
]
] |
solv-int/9509009 | Yunbo Zeng | Yunbo Zeng | The separability and dynamical $r$-matrix for the constrained flows of
Jaulent-Miodek hierarchy | 12 pages in LaTeX | null | null | null | solv-int nlin.SI | null | We show here the separability of Hamilton-Jacobi equation for a hierarchy of
integrable Hamiltonian systems obtained from the constrained flows of the
Jaulent-Miodek hierarchy. The classical Poisson structure for these Hamiltonian
systems is constructed. The associated $r$-matrices depend not only on the
spectral parameters, but also on the dynamical variables and, for consistency,
have to obey the classical Yang-Baxter equations of dynamical type. Some new
solutions of classical dynamical Yang-Baxter equations are presented. Thus
these integrable systems provide examples both for the dynamical $r$-matrix and
for the separable Hamiltonian system not having a natural Hamiltonian form.
| [
{
"version": "v1",
"created": "Mon, 25 Sep 1995 13:59:54 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Zeng",
"Yunbo",
""
]
] |
solv-int/9509010 | Piotr G. Grinevich | P.G.Grinevich (Landau Institute for Theoretical Physics, Moscow,
Russia) | Nonsingularity of the direct scattering transform for the KP-2 equation
with real exponentially decaying at infinity potential | 19 pages, LaTeX, 1 picture in PostScript format included in the end
of the paper and 3 style files | null | null | null | solv-int nlin.SI | null | We study the direct spectral transform for the heat equation, associated with
the KP-2 equation. We show, that for real nonsingular exponentially decaying at
infinity potentials the direct problem is nonsingular for arbitrary large
potentials. Earlier this statement was proved only for potentials, satisfying
the ``small norm'' assumption.
| [
{
"version": "v1",
"created": "Mon, 25 Sep 1995 21:22:09 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Grinevich",
"P. G.",
"",
"Landau Institute for Theoretical Physics, Moscow,\n Russia"
]
] |
solv-int/9509011 | Sello Dmp | S. Sello (Cise-Innovative Technologies, Milan Italy) | Nonlinear Behaviour of Time-Stepping Algorithms for Initial Value
Problems | uuencoded compressed postscript file, 12 pages paper with included
figures. (source file: 3.1 Mb) | null | null | CISE-SMA950919 | solv-int nlin.SI | null | Recent advances in nonlinear dynamical systems theory provide a new insight
into numerical properties of discrete algorithms developed to solve nonlinear
initial value problems. Basic features like accuracy and stability are well
pointed out through diagrams or maps of computed asymptotic solutions in a
suitable parametric space. Applying this methodology to a nonlinear test
equation, we compared some numerical features of the well known second-order
Crank-Nicolson solver with those of a recent proposed version which is
fourth-order accurate. The approach gives some useful indication on the
capabilities of familiar and innovative ODE integrators when applied to
nonlinear problems.
| [
{
"version": "v1",
"created": "Wed, 27 Sep 1995 13:50:01 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Sello",
"S.",
"",
"Cise-Innovative Technologies, Milan Italy"
]
] |
solv-int/9509012 | null | O.Ragnisco (Phys. Dept. Univ. Rome III), M.Bruschi (Phys. Dep. Univ.
Rome "La Sapienza") | Peakons, R-Matrix and Toda-Lattice | 12 plain tex pages | null | 10.1016/0378-4371(95)00438-6 | null | solv-int nlin.SI | null | The integrability of a family of hamiltonian systems, describing in a
particular case the motionof N ``peakons" (special solutions of the so-called
Camassa-Holm equation) is established in the framework of the $r$-matrix
approach, starting from its Lax representation. In the general case, the
$r$-matrix is a dynamical one and has an interesting though complicated
structure. However, for a particular choice of the relevant parameters in the
hamiltonian (the one corresponding to the pure ``peakons" case), the $r$-matrix
becomes essentially constant, and reduces to the one pertaining to the finite
(non-periodic) Toda lattice. Intriguing consequences of such property are
discussed and an integrable time discretisation is derived.
| [
{
"version": "v1",
"created": "Thu, 28 Sep 1995 14:00:56 GMT"
}
] | 2015-06-26T00:00:00 | [
[
"Ragnisco",
"O.",
"",
"Phys. Dept. Univ. Rome III"
],
[
"Bruschi",
"M.",
"",
"Phys. Dep. Univ.\n Rome \"La Sapienza\""
]
] |
solv-int/9510001 | Peter Nattermann | P. Nattermann and R. Zhdanov | On Integrable Doebner-Goldin Equations | 23 pages, revtex, 1 figure, uses epsfig.sty and amssymb.sty | J.Phys.A29:2869-2886,1996 | 10.1088/0305-4470/29/11/021 | ASI-TPA/8/95 | solv-int hep-th nlin.SI quant-ph | null | We suggest a method for integrating sub-families of a family of nonlinear
{\sc Schr\"odinger} equations proposed by {\sc H.-D.~Doebner} and {\sc
G.A.~Goldin} in the 1+1 dimensional case which have exceptional {\sc Lie}
symmetries. Since the method of integration involves non-local transformations
of dependent and independent variables, general solutions obtained include
implicitly determined functions. By properly specifying one of the arbitrary
functions contained in these solutions, we obtain broad classes of explicit
square integrable solutions. The physical significance and some analytical
properties of the solutions obtained are briefly discussed.
| [
{
"version": "v1",
"created": "Tue, 10 Oct 1995 09:46:27 GMT"
}
] | 2008-11-26T00:00:00 | [
[
"Nattermann",
"P.",
""
],
[
"Zhdanov",
"R.",
""
]
] |
solv-int/9510002 | Benjamin Enriquez | B. Enriquez, A.Yu. Orlov, V.N. Rubtsov | Dispersionful analogues of Benney's equations and $N$-wave systems | 12 pages, latex, no figures | null | 10.1088/0266-5611/12/3/005 | null | solv-int hep-th nlin.SI | null | We recall Krichever's construction of additional flows to Benney's hierarchy,
attached to poles at finite distance of the Lax operator. Then we construct a
``dispersionful'' analogue of this hierarchy, in which the role of poles at
finite distance is played by Miura fields. We connect this hierarchy with
$N$-wave systems, and prove several facts about the latter (Lax representation,
Chern-Simons-type Lagrangian, connection with Liouville equation,
$\tau$-functions).
| [
{
"version": "v1",
"created": "Wed, 11 Oct 1995 14:02:59 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Enriquez",
"B.",
""
],
[
"Orlov",
"A. Yu.",
""
],
[
"Rubtsov",
"V. N.",
""
]
] |
solv-int/9510003 | Leon Jerome | J. Leon, (Physique Mathematique et Theorique, Montpellier-France) | Solution of SRS on the finite interval | Revised version, Submitted to Phys. Lett. A, revtex, NO figure | null | null | null | solv-int nlin.SI | null | The equations of transient stimulated Raman scattering on the finite interval
are solved by the spectral transform method on the semi-line. As the problem
has a free end, the pump and Stokes output at finite distance can be
constructed as the solution of a linear Cauchy-Green integral equation.
| [
{
"version": "v1",
"created": "Mon, 16 Oct 1995 08:31:02 GMT"
},
{
"version": "v2",
"created": "Fri, 27 Oct 1995 15:30:04 GMT"
},
{
"version": "v3",
"created": "Thu, 22 Feb 1996 14:59:24 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Leon",
"J.",
""
]
] |
solv-int/9510004 | Richard Ward | R. S. Ward | Nontrivial scattering of localized solitons in a (2+1)-dimensional
integrable system | 9 pages, plainTeX, figure not included To appear in Physics Letters A | null | 10.1016/0375-9601(95)00782-X | DTP95/59 | solv-int nlin.SI | null | One usually expects localized solitons in integrable systems to interact
trivially. There is an integrable (2+1)-dimensional chiral equation which
admits multi-soliton solutions with trivial dynamics. This paper describes how
to generate explicit solutions representing nontrivial soliton interactions: in
particular, a head-on collision of two solitons resulting in $90^\circ$
scattering.
| [
{
"version": "v1",
"created": "Tue, 17 Oct 1995 16:06:07 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Ward",
"R. S.",
""
]
] |
solv-int/9510005 | Richard Ward | T. Ioannidou and R. S. Ward | Conserved quantities for integrable chiral equations in 2+1 dimensions | 10 pages, plainTeX, to appear in Physics Letters A | null | 10.1016/0375-9601(95)00781-W | DTP95/57 | solv-int nlin.SI | null | The integrable (2+1)-dimensional chiral equations are related to the
self-dual Yang-Mills equation. Previously-known nonlocal conservation laws do
not yield finite conserved charges, because the relevant spatial integrals
diverge. We exhibit infinite sequences of conserved quantities that do exist,
and have a simple explicit form.
| [
{
"version": "v1",
"created": "Tue, 17 Oct 1995 16:25:58 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Ioannidou",
"T.",
""
],
[
"Ward",
"R. S.",
""
]
] |
solv-int/9510006 | Saburo Kakei | Saburo Kakei | Toda Lattice Hierarchy and Zamolodchikov's Conjecture | 6 pages, LaTeX file, no figures | null | 10.1143/JPSJ.65.337 | null | solv-int hep-th nlin.SI | null | In this letter, we show that certain Fredholm determinant $D(\lambda;t)$,
introduced by Zamolodchikov in his study of 2D polymers, is a continuum limit
of soliton solution for the Toda lattice hierarchy with 2-periodic reduction
condition.
| [
{
"version": "v1",
"created": "Mon, 23 Oct 1995 10:14:42 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Kakei",
"Saburo",
""
]
] |
solv-int/9510007 | Juri Suris | Yuri B. Suris (University of Bremen, Germany) | A discrete time relativistic Toda lattice | 32 pages, LaTeX | J. Phys. A: Math. and Gen., 1996, V. 29, p. 451-465. | 10.1088/0305-4470/29/2/022 | null | solv-int nlin.SI | null | Four integrable symplectic maps approximating two Hamiltonian flows from the
relativistic Toda hierarchy are introduced. They are demostrated to belong to
the same hierarchy and to examplify the general scheme for symplectic maps on
groups equiped with quadratic Poisson brackets. The initial value problem for
the difference equations is solved in terms of a factorization problem in a
group. Interpolating Hamiltonian flows are found for all the maps.
| [
{
"version": "v1",
"created": "Mon, 23 Oct 1995 14:42:07 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Suris",
"Yuri B.",
"",
"University of Bremen, Germany"
]
] |
solv-int/9510008 | null | Petro Holod and Sergey Kondratiuk | The Orbit Method in the Finite Zone Integration Theory | 12 pages, no figures, LaTeX, a contrubution to the XII Hutsulian
Workshop "Methods of Mathematical Physics", Rakhov, 1995, september 11-17 | null | null | null | solv-int hep-th nlin.SI | null | A construction of integrable hamiltonian systems associated with different
graded realizations of untwisted loop algebras is proposed. Such systems have
the form of Euler - Arnold equations on orbits of loop algebras. The proof of
completeness of the integrals of motion is carried out independently of the
realization of the loop algebra. The hamiltonian systems obtained are shown to
coincide with hierarchies of higher stationary equations for some nonlinear
PDE's integrable by inverse scattering method.
We apply the general scheme for the principal and homogeneous realizations of
the loop algebra $ sl_3(\R)\otimes{\cal P}(\lambda,\lambda^{-1}) $. The
corresponding equations on the degenerated orbit are interpreted as the
Boussinesq's and two-component modified KDV equations respectively. The scalar
Lax representation for the Boussinesq's equation is found in terms of
coordinates on the orbit applying the Drinfeld - Sokolov reduction procedure.
| [
{
"version": "v1",
"created": "Mon, 23 Oct 1995 13:45:05 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Holod",
"Petro",
""
],
[
"Kondratiuk",
"Sergey",
""
]
] |
solv-int/9510009 | Henrik Aratyn | H. Aratyn, E. Nissimov and S. Pacheva | On Integrable Models and their Interrelations | LaTeX, 9 pgs, Talk given at the Theoretical Physics Symposium in
honor of Paulo Leal Ferreira (S\~{a}o Paulo, August 7-11,1995) | null | null | UICHEP-TH/95-11 | solv-int nlin.SI | null | We present an elementary discussion of the Calogero-Moser model. This gives
us an opportunity to illustrate basic concepts of the dynamical integrable
models. Some ideas are also presented regarding interconnections between
integrable models based on the relation established between the Calogero-Moser
model and the truncated KP hierarchy of Burgers-Hopf type.
| [
{
"version": "v1",
"created": "Mon, 23 Oct 1995 22:03:23 GMT"
},
{
"version": "v2",
"created": "Mon, 30 Oct 1995 17:21:33 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Aratyn",
"H.",
""
],
[
"Nissimov",
"E.",
""
],
[
"Pacheva",
"S.",
""
]
] |
solv-int/9510010 | Basile Grammaticos | B. Grammaticos and A. Ramani | The Gambier Mapping | PlainTeX | null | 10.1016/0378-4371(95)00213-8 | null | solv-int nlin.SI | null | We propose a discrete form for an equation due to Gambier and which belongs
to the class of the fifty second order equations that possess the Painleve
property. In the continuous case, the solutions of the Gambier equation is
obtained through a system of Riccati equations. The same holds true in the
discrete case also. We use the singularity confinement criterion in order to
study the integrability of this new mapping.
| [
{
"version": "v1",
"created": "Mon, 30 Oct 1995 13:57:59 GMT"
}
] | 2015-06-26T00:00:00 | [
[
"Grammaticos",
"B.",
""
],
[
"Ramani",
"A.",
""
]
] |
solv-int/9510011 | Basile Grammaticos | A. Ramani and B. Grammaticos | Discrete Painleve equations: coalescences, limits and degeneracies | PlainTeX | null | 10.1016/0378-4371(95)00439-4 | null | solv-int nlin.SI | null | Starting from the standard form of the five discrete Painlev\'e equations we
show how one can obtain (through appropriate limits) a host of new equations
which are also the discrete analogues of the continuous Painlev\'e equations. A
particularly interesting technique is the one based on the assumption that some
simplification takes place in the autonomous form of the mapping following
which the deautonomization leads to a new $n$-dependence and introduces more
new discrete Painlev\'e equations.
| [
{
"version": "v1",
"created": "Thu, 2 Nov 1995 16:46:04 GMT"
}
] | 2015-06-26T00:00:00 | [
[
"Ramani",
"A.",
""
],
[
"Grammaticos",
"B.",
""
]
] |
solv-int/9510012 | Wen-Xiu Ma | Wen-Xiu Ma, Benno Fuchssteiner and Walter Oevel (Paderborn University,
Germany) | A three-by-three matrix spectral problem for AKNS hierarchy and its
binary Nonlinearization | 21pages, in Latex | null | 10.1016/S0378-4371(96)00225-7 | null | solv-int hep-th nlin.SI | null | A three-by-three matrix spectral problem for AKNS soliton hierarchy is
proposed and the corresponding Bargmann symmetry constraint involved in Lax
pairs and adjoint Lax pairs is discussed. The resulting nonlinearized Lax
systems possess classical Hamiltonian structures, in which the nonlinearized
spatial system is intimately related to stationary AKNS flows. These
nonlinearized Lax systems also lead to a sort of involutive solutions to each
AKNS soliton equation.
| [
{
"version": "v1",
"created": "Thu, 2 Nov 1995 22:35:37 GMT"
}
] | 2015-06-26T00:00:00 | [
[
"Ma",
"Wen-Xiu",
"",
"Paderborn University,\n Germany"
],
[
"Fuchssteiner",
"Benno",
"",
"Paderborn University,\n Germany"
],
[
"Oevel",
"Walter",
"",
"Paderborn University,\n Germany"
]
] |
solv-int/9511001 | Atsushi SLIME Nagai | Atsushi Nagai and Junkichi Satsuma | Discrete soliton equations and convergence acceleration algorithms | 11 pages, LaTeX file, no figures | null | 10.1016/0375-9601(95)00865-9 | null | solv-int nlin.SI | null | Some of the well-known convergence acceleration algorithms, when viewed as
two-variable difference equations, are equivalent to discrete soliton
equations. It is shown that the $\eta-$algorithm is nothing but the discrete
KdV equation. In addition, one generalized version of the $\rho-$algorithm is
considered to be integrable discretization of the cylindrical KdV equation.
| [
{
"version": "v1",
"created": "Tue, 7 Nov 1995 11:31:47 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Nagai",
"Atsushi",
""
],
[
"Satsuma",
"Junkichi",
""
]
] |
solv-int/9511002 | Garcia Ariel | Ariel O. Garcia and Roberto C. Trinchero | Constructive building of the Lax pair in the non-linear sigma model | 10 pages, LaTeX2e and AMSLaTeX, no extra macros, one latex figure | J.Math.Phys. 37 (1996) 3973-3981 | 10.1063/1.531610 | null | solv-int hep-th nlin.SI | null | A derivation of the Lax pair for the (1+1)-dimensional non-linear sigma-model
is described. Its main benefit is to have a clearer physical origin and to
allow the study of a generalization to higher dimensions.
| [
{
"version": "v1",
"created": "Tue, 7 Nov 1995 14:26:03 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Garcia",
"Ariel O.",
""
],
[
"Trinchero",
"Roberto C.",
""
]
] |
solv-int/9511003 | Helge Frauenkron | Alessandro Torcini, Helge Frauenkron, Peter Grassberger (Theoretische
Physik, Bergische Universit\"at-Gesamthochschule Wuppertal, Wuppertal,
Germany) | A Novel Integration Scheme for Partial Differential Equations: an
Application to the Complex Ginzburg-Landau Equation | 10 pages Postscript + 2 figures, uudecoded, gzipped, tarred submitted
to Physica D | null | null | null | solv-int nlin.SI | null | A new integration scheme, combining the stability and the precision of usual
pseudo-spectral codes with the locality of finite differences methods, is
introduced. It turns out to be particularly suitable for the study of front and
disturbance propagation in extended systems. An application to the complex
Ginzburg-Landau equation shows the higher precision of this method with respect
to spectral ones.
| [
{
"version": "v1",
"created": "Thu, 9 Nov 1995 15:58:58 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Torcini",
"Alessandro",
"",
"Theoretische\n Physik, Bergische Universität-Gesamthochschule Wuppertal, Wuppertal,\n Germany"
],
[
"Frauenkron",
"Helge",
"",
"Theoretische\n Physik, Bergische Universität-Gesamthochschule Wuppertal, Wuppertal,\n Germany"
],
[
"Grassberger",
"Peter",
"",
"Theoretische\n Physik, Bergische Universität-Gesamthochschule Wuppertal, Wuppertal,\n Germany"
]
] |
solv-int/9511004 | Latypov A. M. | Azat M. Latypov | Approximate Lie Group Analysis of Finite-difference Equations | 21 pages, LaTeX | null | null | null | solv-int nlin.SI | null | Approximate group analysis technique, that is, the technique combining the
methodology of group analysis and theory of small perturbations, is applied to
finite-difference equations approximating ordinary differential equations.
Finite-difference equations are viewed as a system of algebraic equations with
a small parameter, introduced through the definitions of finite-difference
derivatives. It is shown that application of the approximate invariance
criterion to this algebraic system results in relations that can be viewed as
prolongation formulae and the invariance criterion for the differential
approximation of these finite-difference equations. This allows us to study the
group properties of the finite-difference equations by analyzing the group
properties of their differential approximations, which are the differential
equations with a small parameter. In particular, the question of whether the
group, admitted by the original differential equation, can be corrected by
adding the first-order perturbation to it, so that the resulting group with a
small parameter is approximately admitted by the finite-difference
approximation, is studied. It is shown by examples that, for a given
differential equation, its finite--difference approximation and the group, such
a correction may not always be possible. It is also demonstrated that the
finite--difference approximation can be modified in such a way that the
correction becomes possible.
| [
{
"version": "v1",
"created": "Thu, 9 Nov 1995 21:12:09 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Latypov",
"Azat M.",
""
]
] |
solv-int/9511005 | Wen-Xiu Ma | Wen-Xiu Ma, Benno Fuchssteiner | Explicit and Exact Solutions to a Kolmogorov-Petrovskii-Piskunov
Equation | 14pages, Latex, to appear in Intern. J. Nonlinear Mechanics, the
original latex file is not complete | null | 10.1016/0020-7462(95)00064-X | null | solv-int nlin.SI | null | Some explicit traveling wave solutions to a Kolmogorov-Petrovskii-Piskunov
equation are presented through two ans\"atze. By a Cole-Hopf transformation,
this Kolmogorov-Petrovskii-Piskunov equation is also written as a bilinear
equation and further two solutions to describe nonlinear interaction of
traveling waves are generated. B\"acklund transformations of the linear form
and some special cases are considered.
| [
{
"version": "v1",
"created": "Tue, 14 Nov 1995 16:41:05 GMT"
},
{
"version": "v2",
"created": "Thu, 30 Nov 1995 18:01:48 GMT"
},
{
"version": "v3",
"created": "Fri, 1 Dec 1995 14:21:48 GMT"
}
] | 2019-08-15T00:00:00 | [
[
"Ma",
"Wen-Xiu",
""
],
[
"Fuchssteiner",
"Benno",
""
]
] |
solv-int/9511006 | Ravil I. Yamilov | D. Levi, R. Yamilov | Classification of evolutionary equations on the lattice. I. The general
theory | 24 pages, AmsTeX | null | null | null | solv-int nlin.SI | null | A modification of the symmetry approach for the classification of integrable
differential-difference equations of the form $$ u_{n,t} = f_n(u_{n-1}, u_n,
u_{n+1}), $$ where $n$ is a discrete integer variable, is presented (the
well-known Volterra and Toda equations can be written in this form). If before,
in the framework of the symmetry approach, only equations similar to $$ u_{n,t}
= f(u_{n-1}, u_n, u_{n+1}), $$ i.e. defined by a function $f$, were considered,
now we have an infinite set $f_n$ of a priori quite different functions.
| [
{
"version": "v1",
"created": "Thu, 16 Nov 1995 09:58:04 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Levi",
"D.",
""
],
[
"Yamilov",
"R.",
""
]
] |
solv-int/9511007 | Ayrton Zadra | L.E. Saltini and A. Zadra | Algebra of Non-Local Charges in Supersymmetric Non-Linear Sigma Models | LateX file, 19 pages, figures included with epsf; file with figures
has been replaced | Int.J.Mod.Phys. A12 (1997) 419-436 | 10.1142/S0217751X97000487 | IFUSP/P-1188 | solv-int hep-th nlin.SI | null | We propose a graphic method to derive the classical algebra (Dirac brackets)
of non-local conserved charges in the two dimensional supersymmetric non-linear
$O(N)$ sigma model. As in the purely bosonic theory we find a cubic Yangian
algebra. We also consider the extension of graphic methods to other integrable
theories.
| [
{
"version": "v1",
"created": "Thu, 16 Nov 1995 19:21:32 GMT"
},
{
"version": "v2",
"created": "Fri, 17 Nov 1995 13:04:09 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Saltini",
"L. E.",
""
],
[
"Zadra",
"A.",
""
]
] |
solv-int/9511008 | null | E. Alfinito, G. Profilo, G. Soliani | Properties of equations of the continuous Toda type | LaTex file, 27 pages | J.Phys.A30:1527-1547,1997 | 10.1088/0305-4470/30/5/019 | null | solv-int gr-qc hep-th nlin.SI | null | We study a modified version of an equation of the continuous Toda type in 1+1
dimensions. This equation contains a friction-like term which can be switched
off by annihilating a free parameter $\ep$. We apply the prolongation method,
the symmetry and the approximate symmetry approach. This strategy allows us to
get insight into both the equations for $\ep =0$ and $\ep \ne 0$, whose
properties arising in the above frameworks are mutually compared. For $\ep =0$,
the related prolongation equations are solved by means of certain series
expansions which lead to an infinite- dimensional Lie algebra. Furthermore,
using a realization of the Lie algebra of the Euclidean group $E_{2}$, a
connection is shown between the continuous Toda equation and a linear wave
equation which resembles a special case of a three-dimensional wave equation
that occurs in a generalized Gibbons-Hawking ansatz \cite{lebrun}. Nontrivial
solutions to the wave equation expressed in terms of Bessel functions are
determined.
For $\ep\,\ne\,0,$ we obtain a finite-dimensional Lie algebra with four
elements. A matrix representation of this algebra yields solutions of the
modified continuous Toda equation associated with a reduced form of a
perturbative Liouville equation. This result coincides with that achieved in
the context of the approximate symmetry approach. Example of exact solutions
are also provided. In particular, the inverse of the exponential-integral
function turns out to be defined by the reduced differential equation coming
from a linear combination of the time and space translations. Finally, a Lie
algebra characterizing the approximate symmetries is discussed.
| [
{
"version": "v1",
"created": "Thu, 23 Nov 1995 10:21:29 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Alfinito",
"E.",
""
],
[
"Profilo",
"G.",
""
],
[
"Soliani",
"G.",
""
]
] |
solv-int/9511009 | Robert Carroll | Robert Carroll (Mathematics Department, University of Illinois,
Urbana, IL) | Remarks on the Whitham equations | Latex, 81 pages, run three times for table of contents | null | null | null | solv-int hep-th nlin.SI | null | We survey some topics involving the Whitham equations, concentrating on the
role of the product of the wave function and its adjoint in averaging and in
producing Cauchy kernels and differentials on Riemann surfaces. There are also
some new results.
| [
{
"version": "v1",
"created": "Fri, 24 Nov 1995 13:28:44 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Carroll",
"Robert",
"",
"Mathematics Department, University of Illinois,\n Urbana, IL"
]
] |
Subsets and Splits