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timestamp[s] | authors_parsed
sequence |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
solv-int/9611007 | YuKui. Zhou | Y.-K. Zhou and K. D. Schotte | The L-Matrix for the Massive Thirring Model | 10 pages, no ps figures, Tex file | Phys Rev D 47 (1993) R1281-R1284 | 10.1103/PhysRevD.47.R1281 | null | solv-int nlin.SI | null | As the new results for the massive Thirring model the L-matrix and the
algebraic relations for its action angle variables are given. So it is shown
most directly that this model which describes self-interacting relativistic
Fermions in one-dimensional space is a quantum integrable system.
| [
{
"version": "v1",
"created": "Tue, 26 Nov 1996 07:32:42 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Zhou",
"Y. -K.",
""
],
[
"Schotte",
"K. D.",
""
]
] |
solv-int/9611008 | Andrei Mal'tsev | A.Ya. Maltsev | The conservation of the Hamiltonian structures in Whitham's method of
averaging | 39 pages, some improvement, corrected misprints | Izvestiya, Mathematics 63:6 (1999), 1171-1201 | null | null | solv-int hep-th nlin.SI | null | The work is devoted to the proof of the conservation of local
field-theoretical Hamiltonian structures in Whitham's method of averaging. The
consideration is based on the procedure of averaging of local Poisson bracket,
proposed by B.A.Dubrovin and S.P.Novikov. Using the Dirac procedure of
restriction of the Poisson bracket on the submanifold in the functional space,
it is shown in the generic case that the Poisson bracket, constructed by method
of Dubrovin and Novikov, satisfies the Jacobi identity. Besides that, the
invariance of this bracket with respect to the choice of the set of local
conservation laws, used in this procedure, is proved.
| [
{
"version": "v1",
"created": "Thu, 28 Nov 1996 18:20:46 GMT"
},
{
"version": "v2",
"created": "Tue, 5 Oct 1999 07:45:17 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Maltsev",
"A. Ya.",
""
]
] |
solv-int/9612001 | Uwe Grimm | Uwe Grimm | Representations of Two-Colour BWM Algebras and Solvable Lattice Models | 6 pages, LaTeX, heron2e.sty (included), Poster presented at GROUP21 | Proceedings of the Quantum Group Symposium at the XXI
International Colloquium on Group Theoretical Methods in Physics, edited by
H.-D. Doebner and V.K. Dobrev, Heron Press, Sofia (1997), pp. 114-119 | null | null | solv-int nlin.SI | null | Many of the known solutions of the Yang-Baxter equation, which are related to
solvable lattice models of vertex- and IRF-type, yield representations of the
Birman-Wenzl-Murakami algebra. From these, representations of a two-colour
generalization of the Birman-Wenzl-Murakami algebra can be constructed, which
in turn are used to derive trigonometric solutions to the Yang-Baxter equation.
In spirit, this construction resembles the fusion procedure, in the sense that
starting from known solutions of the Yang-Baxter equation new solutions can be
obtained.
| [
{
"version": "v1",
"created": "Tue, 3 Dec 1996 11:15:18 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Grimm",
"Uwe",
""
]
] |
solv-int/9612002 | Nicolai Kitanine | N.M. Bogoliubov, A.G. Izergin, N.A. Kitanine | Correlators of the phase model | LaTeX, 7 pages, One reference has been changed | null | 10.1016/S0375-9601(97)00326-5 | ENSLAPP-L-622/96, HU-TFT-96-41 | solv-int nlin.SI | null | We introduce the phase model on a lattice and solve it using the algebraic
Bethe ansatz. Time-dependent temperature correlation functions of phase
operators and the "darkness formation probability" are calculated in the
thermodynamical limit. These results can be used to construct integrable
equations for the correlation functions and to calculate there asymptotics.
| [
{
"version": "v1",
"created": "Wed, 4 Dec 1996 17:12:42 GMT"
},
{
"version": "v2",
"created": "Fri, 20 Dec 1996 14:59:37 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Bogoliubov",
"N. M.",
""
],
[
"Izergin",
"A. G.",
""
],
[
"Kitanine",
"N. A.",
""
]
] |
solv-int/9612003 | Zora Thomova | Z. Thomova, P. Winternitz, W.J. Zakrzewski | Solutions of (2+1)-dimensional spin systems | TeX and phyzzx, 33 pages | J.Math.Phys. 39, 3927-3944 (1998) | 10.1063/1.532476 | CRM-2373 | solv-int hep-th math-ph math.MP nlin.SI | null | We use the methods of group theory to reduce the equations of motion of two
spin systems in (2+1) dimensions to sets of coupled ordinary differential
equations. We present solutions of some classes of these sets and discuss their
physical significance.
| [
{
"version": "v1",
"created": "Wed, 4 Dec 1996 16:40:47 GMT"
}
] | 2017-08-11T00:00:00 | [
[
"Thomova",
"Z.",
""
],
[
"Winternitz",
"P.",
""
],
[
"Zakrzewski",
"W. J.",
""
]
] |
solv-int/9612004 | Alexander V. Razumov | A. V. Razumov, M. V. Saveliev | Riemannian Manifolds with Diagonal Metric. The Lam\'e and Bourlet
Systems | LaTeX file, 22 pages, to appear in the proceedings of the
international conference "Selected Topics of Theoretical and Modern
Mathematical Physics (SIMI-96)", September 22-29, 1996, Tbilisi, Georgia | null | null | null | solv-int dg-ga hep-th math.DG nlin.SI | null | We discuss a Lie algebraic and differential geometry construction of
solutions to some multidimensional nonlinear integrable systems describing
diagonal metrics on Riemannian manifolds, in particular those of zero and
constant curvature. Here some special solutions to the Lam\'e and Bourlet type
equations, determining by n arbitrary functions of one variable are obtained in
an explicit form. For the case when the sum of the diagonal elements of the
metric is a constant, these solutions are expressed as a product of the Jacobi
elliptic functions and are determined by 2n arbitrary constants.
| [
{
"version": "v1",
"created": "Sun, 8 Dec 1996 13:03:23 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Razumov",
"A. V.",
""
],
[
"Saveliev",
"M. V.",
""
]
] |
solv-int/9612005 | Ryuji Kemmoku 0426-77-1111x3377 | Ryuji Kemmoku | Difference Operator Approach to the Moyal Quantization and Its
Application to Integrable Systems | 19 pages, to appear in J. Phys. Soc. Jpn | null | 10.1143/JPSJ.66.51 | TMUP-HEL-9609 | solv-int nlin.SI | null | Inspired by the fact that the Moyal quantization is related with nonlocal
operation, I define a difference analogue of vector fields and rephrase quantum
description on the phase space. Applying this prescription to the theory of the
KP-hierarchy, I show that their integrability follows to the nature of their
Wigner distribution. Furthermore the definition of the ``expectation value''
clarifies the relation between our approach and the Hamiltonian structure of
the KP-hierarchy. A trial of the explicit construction of the Moyal bracket
structure in the integrable system is also made.
| [
{
"version": "v1",
"created": "Wed, 11 Dec 1996 11:55:02 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Kemmoku",
"Ryuji",
""
]
] |
solv-int/9612006 | Adam Doliwa | A. Doliwa | Geometric Discretisation of the Toda System | 12 pages, LaTeX, 2 Postscript figures | Phys. Lett. A 234 (1997) 187. | 10.1016/S0375-9601(97)00477-5 | ROME1-1160/96 | solv-int hep-lat hep-th nlin.SI | null | The Laplace sequence of the discrete conjugate nets is constructed. The
invariants of the nets satisfy, in full analogy to the continuous case, the
system of difference equations equivalent to the discrete version of the
generalized Toda equation.
| [
{
"version": "v1",
"created": "Thu, 19 Dec 1996 15:54:49 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Doliwa",
"A.",
""
]
] |
solv-int/9612007 | Adam Doliwa | A. Doliwa and P. M. Santini | Multidimensional Quadrilateral Lattices are Integrable | 18 pages, LaTeX, 6 Postscript figures | Phys. Lett. A 233 (1997) 365. | 10.1016/S0375-9601(97)00456-8 | ROME1-1162/96 | solv-int hep-lat nlin.SI | null | The notion of multidimensional quadrilateral lattice is introduced. It is
shown that such a lattice is characterized by a system of integrable discrete
nonlinear equations. Different useful formulations of the system are given. The
geometric construction of the lattice is also discussed and, in particular, it
is clarified the number of initial--boundary data which define the lattice
uniquely.
| [
{
"version": "v1",
"created": "Thu, 19 Dec 1996 17:02:07 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Doliwa",
"A.",
""
],
[
"Santini",
"P. M.",
""
]
] |
solv-int/9612008 | Jaroslav Dittrich | J. Dittrich, V. I. Inozemtsev | On the two-magnon bound states for the quantum Heisenberg chain with
variable range exchange | 8 pages, latex, no figures | null | 10.1142/S0217984997000554 | null | solv-int cond-mat.stat-mech nlin.SI | null | The spectrum of finite-difference two-magnon operator is investigated for
quantum S=1/2 chain with variable range exchange of the form $h(j-k)\propto
\sinh^{-2}a(j-k)$. It is found that usual bound state appears for some values
of the total pseudomomentum of two magnons as for the Heisenberg chain with
nearest-neighbor spin interaction. Besides this state, a new type of bound
state with oscillating wave function appears at larger values of the total
pseudomomentum.
| [
{
"version": "v1",
"created": "Fri, 20 Dec 1996 09:31:03 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Dittrich",
"J.",
""
],
[
"Inozemtsev",
"V. I.",
""
]
] |
solv-int/9612009 | Yves Brihaye | Y. Brihaye, S. Giller, P. Kosinski, J. Nuyts | Irreducible Representations of an Algebra underlying Hidden Symmetries
of a class of Quasi Exactly Solvable Systems of Equations | 38 pages, latex | null | 10.1007/s002200050133 | null | solv-int nlin.SI | null | The set of linear, differential operators preserving the vector space of
couples of polynomials of degrees n and n-2 in one real variable leads to an
abstract associative graded algebra A(2). The irreducible, finite dimensional
representations of this algebra are classified into five infinite discrete sets
and one exceptional case. Their matrix elements are given explicitely. The
results are related to the theory of quasi exactly solvable equations.
| [
{
"version": "v1",
"created": "Fri, 20 Dec 1996 16:36:12 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Brihaye",
"Y.",
""
],
[
"Giller",
"S.",
""
],
[
"Kosinski",
"P.",
""
],
[
"Nuyts",
"J.",
""
]
] |
solv-int/9612010 | Robert Carroll | R. Carroll and J. Chang (Mathematics Dept., University of Illinois,
Urbana, IL) | The Whitham equations revisited | Latex 40 pages | null | null | null | solv-int nlin.SI | null | We survey some topics involving the Whitham equations, concentrating on the
role of the Baker Akhiezer function in averaging. Some connections to
symplectic geometry and Seiberg-Witten theory are indicated.
| [
{
"version": "v1",
"created": "Tue, 24 Dec 1996 14:04:20 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Carroll",
"R.",
"",
"Mathematics Dept., University of Illinois,\n Urbana, IL"
],
[
"Chang",
"J.",
"",
"Mathematics Dept., University of Illinois,\n Urbana, IL"
]
] |
solv-int/9612011 | Robert Carroll | R. Carroll (Mathematics Dept., University of Illinois, Urbana, IL) | Some kernels on a Riemann surface | Latex 22 pages | null | null | null | solv-int nlin.SI | null | We discuss certain kernels on a Riemann surface, constructed mainly via Baker
Akhiezer functions, and indicate relations to dispersionless theory.
| [
{
"version": "v1",
"created": "Tue, 24 Dec 1996 14:08:21 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Carroll",
"R.",
"",
"Mathematics Dept., University of Illinois, Urbana, IL"
]
] |
solv-int/9612012 | John Harnad | J. Harnad | Bispectral Operators of Rank 1 and Dual Isomonodromic Deformations | 16pgs, AMSTeX | CRM Proc. Lecture Notes 11, 155-167 (Amer. Math. Soc., Providence
RI, 1997) | null | CRM 2443 (1996) | solv-int hep-th nlin.SI | null | A comparison is made between bispectral operator pairs and dual pairs of
isomonodromic deformation equations. Through examples, it is shown how
operators belonging to rank one bispectral algebras may be viewed equivalently
as defining 1-parameter families of rational first order differential operators
with matricial coefficients on the Riemann sphere, whose monodromy is trivial.
By interchanging the r\^oles of the two variables entering in the bispectral
pair, a second 1-parameter family of operators with trivial monodromy is
obtained, which may be viewed as the dual isomonodromic deformation system.
| [
{
"version": "v1",
"created": "Thu, 26 Dec 1996 23:15:18 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Harnad",
"J.",
""
]
] |
solv-int/9701001 | Arthur Vartanian | A. V. Kitaev and A. H. Vartanian | Leading Order Temporal Asymptotics of the Modified Non-Linear
Schrodinger Equation: Solitonless Sector | 29 pages, 5 figures, LaTeX, revised version of the original
submission, to be published in Inverse Problems | null | 10.1088/0266-5611/13/5/014 | null | solv-int nlin.PS nlin.SI patt-sol physics.plasm-ph | null | Using the matrix Riemann-Hilbert factorisation approach for non-linear
evolution equations (NLEEs) integrable in the sense of the inverse scattering
method, we obtain, in the solitonless sector, the leading-order asymptotics as
$t$ tends to plus and minus infinity of the solution to the Cauchy
initial-value problem for the modified non-linear Schrodinger equation: also
obtained are analogous results for two gauge-equivalent NLEEs; in particular,
the derivative non-linear Schrodinger equation.
| [
{
"version": "v1",
"created": "Fri, 27 Dec 1996 13:18:41 GMT"
},
{
"version": "v2",
"created": "Tue, 24 Jun 1997 15:45:46 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Kitaev",
"A. V.",
""
],
[
"Vartanian",
"A. H.",
""
]
] |
solv-int/9701002 | Jarmo Hietarinta | Jarmo Hietarinta | Painleve equations in terms of entire functions | 22 pages, lectures given at the summer school ``The Painleve
property, one century later'', Cargese, 3-22 June, 1996 | null | null | null | solv-int nlin.SI | null | In these lectures we discuss how the Painleve equations can be written in
terms of entire functions, and then in the Hirota bilinear (or multilinear)
form. Hirota's method, which has been so useful in soliton theory, is reviewed
and connections from soliton equations to Painleve equations through similarity
reductions are discussed from this point of view. In the main part we discuss
how singularity structure of the solutions and formal integration of the
Painleve equations can be used to find a representation in terms of entire
functions. Sometimes the final result is a pair of Hirota bilinear equations,
but for $P_{VI}$ we need also a quadrilinear expression. The use of discrete
versions of Painleve equations is also discussed briefly. It turns out that
with discrete equations one gets better information on the singularities, which
can then be represented in terms of functions with a simple zero.
| [
{
"version": "v1",
"created": "Mon, 30 Dec 1996 10:35:06 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Hietarinta",
"Jarmo",
""
]
] |
solv-int/9701003 | Craig A. Tracy | C. A. Tracy and H. Widom | Asymptotics of a Class of Solutions to the Cylindrical Toda Equations | 29 pages, no figures, LaTeX file | Commun. Math. Phys 190 (1998) 697-721 | 10.1007/s002200050257 | null | solv-int funct-an math.FA nlin.SI | null | The small t asymptotics of a class of solutions to the 2D cylindrical Toda
equations is computed. The solutions, q_k(t), have the representation q_k(t) =
log det(I-lambda K_k) - log det(I-lambda K_{k-1}) where K_k are integral
operators. This class includes the n-periodic cylindrical Toda equations. For
n=2 our results reduce to the previously computed asymptotics of the 2D radial
sinh-Gordon equation and for n=3 (and with an additional symmetry contraint)
they reduce to earlier results for the radial Bullough-Dodd equation.
| [
{
"version": "v1",
"created": "Fri, 10 Jan 1997 04:58:57 GMT"
}
] | 2009-07-13T00:00:00 | [
[
"Tracy",
"C. A.",
""
],
[
"Widom",
"H.",
""
]
] |
solv-int/9701004 | V. Kuznetsov | V.B. Kuznetsov, F.W. Nijhoff and E.K. Sklyanin | Separation of variables for the Ruijsenaars system | 26 pages, LaTex, no figures | Commun.Math.Phys. 189(1997) 855-877 | 10.1007/s002200050231 | CNLS-Leeds preprint, 10 January 1997 | solv-int hep-th math.QA nlin.SI q-alg | null | We construct a separation of variables for the classical n-particle
Ruijsenaars system (the relativistic analog of the elliptic Calogero-Moser
system). The separated coordinates appear as the poles of the properly
normalised eigenvector (Baker-Akhiezer function) of the corresponding Lax
matrix. Two different normalisations of the BA functions are analysed. The
canonicity of the separated variables is verified with the use of r-matrix
technique. The explicit expressions for the generating function of the
separating canonical transform are given in the simplest cases n=2 and n=3.
Taking nonrelativistic limit we also construct a separation of variables for
the elliptic Calogero-Moser system.
| [
{
"version": "v1",
"created": "Fri, 10 Jan 1997 13:59:29 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Kuznetsov",
"V. B.",
""
],
[
"Nijhoff",
"F. W.",
""
],
[
"Sklyanin",
"E. K.",
""
]
] |
solv-int/9701005 | Manuel | Q. P. Liu, M. Manas | Crum Transformations and Wronskian Type Solutions for Supersymmetric KdV
equation | 13 pp, AMS-LaTeX | Phys.Lett.B396:133,1997 | 10.1016/S0370-2693(97)00134-2 | null | solv-int hep-th nlin.SI | null | Darboux transformation is reconsidered for the supersymmetric KdV system. By
iterating the Darboux transformation, a supersymmetric extension of the Crum
transformation is obtained for the Manin-Radul SKdV equation, in doing so one
gets Wronskian superdeterminant representations for the solutions. Particular
examples provide us explicit supersymmetric extensions, super solitons, of the
standard soliton of the KdV equation. The KdV soliton appears as the body of
the super soliton.
| [
{
"version": "v1",
"created": "Fri, 10 Jan 1997 16:12:46 GMT"
}
] | 2008-11-26T00:00:00 | [
[
"Liu",
"Q. P.",
""
],
[
"Manas",
"M.",
""
]
] |
solv-int/9701006 | Luiz Agostinho Ferreira | Luiz A. Ferreira and Joaquin Sanchez Guillen | Aspects of Solitons in Affine Integrable Hierarchies | 39 pages, LaTeX, Two talks presented by the authors at the
``International Workshop on Selected Topics of Theoretical and Modern
Mathematical Physics - SIMI/96'', Tbilisi, Georgia, September/96; Some
misprints corrected in this replaced version | null | null | US-FT/49-96, IFT-P.005/97 | solv-int hep-th nlin.SI | null | We argue that one of the basic ingredients for the appearance of soliton
solutions in integrable hierarchies, is the existence of ``vacuum solutions''
corresponding to Lax operators lying in some abelian subalgebra of the
associated affine Kac-Moody algebra. Using the dressing transformation we
construct the solutions in the orbit of those vacuum solutions, and conjecture
that the solitons correspond to some special points in those orbits. The
generalized tau-function for those hierarchies are defined for integrable
highest weight representations. It applies for any level of the representation.
We illustrate our methods with the recently proposed non abelian Toda models
coupled to matter fields. A very special class of such theories possess a U(1)
Noether charge that is proportional to a topological charge. That leads to a
mechanism that confines the matter fields inside the solitons.
| [
{
"version": "v1",
"created": "Fri, 10 Jan 1997 21:04:43 GMT"
},
{
"version": "v2",
"created": "Fri, 17 Jan 1997 13:32:09 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Ferreira",
"Luiz A.",
""
],
[
"Guillen",
"Joaquin Sanchez",
""
]
] |
solv-int/9701007 | Manuel | Q. P. Liu, M. Manas | Darboux Transformation for the Manin-Radul Supersymmetric KdV equation | 14 pp, 2 figures, AMS-LaTeX, to appear in Phys. Lett. B | Phys. Lett. B, 394 (1997) 337 | 10.1016/S0370-2693(97)00026-9 | null | solv-int hep-th nlin.SI | null | In this paper we present a vectorial Darboux transformation, in terms of
ordinary determinants, for the supersymmetric extension of the Korteweg-de
Vries equation proposed by Manin and Radul. It is shown how this transformation
reduces to the Korteweg-de Vries equation. Soliton type solutions are
constructed by dressing the vacuum and we present some relevant plots.
| [
{
"version": "v1",
"created": "Fri, 10 Jan 1997 17:11:06 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Liu",
"Q. P.",
""
],
[
"Manas",
"M.",
""
]
] |
solv-int/9701008 | Sergei Kharchev | A. Yu. Orlov and P. Winternitz | $P_\infty$ algebra of KP, free fermions and 2-cocycle in the Lie algebra
of pseudodifferential operators | 21 pages, Latex, no figures (some references added and misprints are
corrected) | null | 10.1142/S0217979297001532 | null | solv-int nlin.SI | null | The symmetry algebra $P_\infty = W_\infty \oplus H \oplus I_\infty$ of
integrable systems is defined. As an example the classical Sophus Lie point
symmetries of all higher KP equations are obtained. It is shown that one
(``positive'') half of the point symmetries belongs to the $W_\infty$
symmetries while the other (``negative'') part belongs to the $I_\infty$ ones.
The corresponing action on the tau-function is obtained for the positive part
of the symmetries. The negative part can not be obtained from the free fermion
algebra. A new embedding of the Virasoro algebra into $gl(\infty )$n describes
conformal transformations of the KP time variables. A free fermion algebra
cocycle is described as a PDO Lie algebra cocycle.
| [
{
"version": "v1",
"created": "Mon, 13 Jan 1997 21:39:06 GMT"
},
{
"version": "v2",
"created": "Mon, 3 Feb 1997 23:44:28 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Orlov",
"A. Yu.",
""
],
[
"Winternitz",
"P.",
""
]
] |
solv-int/9701009 | V. Kuznetsov | Vadim B. Kuznetsov | Separation of variables for the Dn type periodic Toda lattice | 15 pages, LaTex, no figures | J Phys A 30 (1997) 2127-2138 | 10.1088/0305-4470/30/6/033 | preprint, University of Leeds, October 1996 | solv-int hep-th nlin.SI | null | We prove separation of variables for the most general (Dn type) periodic Toda
lattice with 2x2 Lax matrix. It is achieved by finding proper normalisation for
the corresponding Baker-Akhiezer function. Separation of variables for all
other periodic Toda lattices associated with infinite series of root systems
follows by taking appropriate limits.
| [
{
"version": "v1",
"created": "Tue, 14 Jan 1997 15:29:46 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Kuznetsov",
"Vadim B.",
""
]
] |
solv-int/9701010 | Juri Suris | Yuri B. Suris (University of Bremen) | A note on the integrable discretization of the nonlinear Schr\"odinger
equation | 24 pages, LaTeX, revised and extended version | Inverse Problems, 1997, V. 13, p. 1121-1136. | 10.1088/0266-5611/13/4/016 | null | solv-int nlin.SI | null | We revisit integrable discretizations for the nonlinear Schr\"odinger
equation due to Ablowitz and Ladik. We demonstrate how their main drawback, the
non-locality, can be overcome. Namely, we factorize the non-local difference
scheme into the product of local ones. This must improve the performance of the
scheme in the numerical computations dramatically. Using the equivalence of the
Ablowitz--Ladik and the relativistic Toda hierarchies, we find the
interpolating Hamiltonians for the local schemes and show how to solve them in
terms of matrix factorizations.
| [
{
"version": "v1",
"created": "Tue, 14 Jan 1997 16:29:43 GMT"
},
{
"version": "v2",
"created": "Tue, 21 Jan 1997 12:32:25 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Suris",
"Yuri B.",
"",
"University of Bremen"
]
] |
solv-int/9701011 | Peter Schupp | Branislav Jurco, Peter Schupp | Twisted Quantum Lax Equations | 23 pages, latex | Int.J.Mod.Phys. A12 (1997) 5735-5752 | 10.1142/S0217751X97003005 | LMU-TPW 97-1, CRM-2448 | solv-int hep-th math.QA nlin.SI q-alg | null | We give the construction of twisted quantum Lax equations associated with
quantum groups. We solve these equations using factorization properties of the
corresponding quantum groups. Our construction generalizes in many respects the
Adler-Kostant-Symes construction for Lie groups and the construction of M. A.
Semenov Tian-Shansky for the Lie-Poisson case.
| [
{
"version": "v1",
"created": "Tue, 21 Jan 1997 09:29:39 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Jurco",
"Branislav",
""
],
[
"Schupp",
"Peter",
""
]
] |
solv-int/9701012 | Luiz Agostinho Ferreira | H.S. Blas Achic, L.A. Ferreira, J.F. Gomes and A.H. Zimerman | Some comments on the bi(tri)-Hamiltonian structure of Generalized AKNS
and DNLS hierarchies | 10 pages, LaTex | Phys.Lett. A237 (1998) 225-233 | 10.1016/S0375-9601(97)00865-7 | IFT-P/006/97 | solv-int nlin.SI | null | We give the correct prescriptions for the terms involving the inverse of the
derivative of the delta function, in the Hamiltonian structures of the AKNS and
DNLS systems, in order for the Jacobi identities to hold. We also establish
that the sl(2) AKNS and DNLS systems are tri-Hamiltonians and construct two
compatible Hamiltonian structures for the sl(3) AKNS system. We also give a
derivation of the recursion operator for the sl(n+1) DNLS system.
| [
{
"version": "v1",
"created": "Mon, 20 Jan 1997 16:37:16 GMT"
}
] | 2015-06-26T00:00:00 | [
[
"Achic",
"H. S. Blas",
""
],
[
"Ferreira",
"L. A.",
""
],
[
"Gomes",
"J. F.",
""
],
[
"Zimerman",
"A. H.",
""
]
] |
solv-int/9701013 | Luiz Agostinho Ferreira | Luiz A. Ferreira | The structures underlying soliton solutions in integrable hierarchies | Talk given at the I Latin American Symposium on High Energy Physics,
I SILAFAE, Merida, Mexico, November/96, 5 pages, LaTeX, needs aipproc.tex,
aipproc.sty, aipproc.cls, available from
ftp://ftp.aip.org/ems/tex/macros/proceedings/6x9/ | null | 10.1063/1.53232 | IFT-P/009/97 | solv-int hep-th nlin.SI | null | We point out that a common feature of integrable hierarchies presenting
soliton solutions is the existence of some special ``vacuum solutions'' such
that the Lax operators evaluated on them, lie in some abelian subalgebra of the
associated Kac-Moody algebra. The soliton solutions are constructed out of
those ``vacuum solitons'' by the dressing transformation procedure.
| [
{
"version": "v1",
"created": "Mon, 20 Jan 1997 17:12:47 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Ferreira",
"Luiz A.",
""
]
] |
solv-int/9701014 | Oleg Kiselev | O.M. Kiselev (Ufa Institute of Mathematics, Russian Acad. of Sci.) | The Fourier method for the linearized Davey-Stewartson I equation | 4 pages, LaTex | Complex analysis, differential equations, numerical methods and
applications. vol.III, Ufa, 1996, p. 93-97, (in russian) | null | null | solv-int nlin.SI | null | The linearized Davey-Stewartson equation with varing coefficients is solved
by Fourier method. The approach uses the inverse scattering transform for the
Davey-Stewartson equation.
| [
{
"version": "v1",
"created": "Mon, 20 Jan 1997 12:07:21 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Kiselev",
"O. M.",
"",
"Ufa Institute of Mathematics, Russian Acad. of Sci."
]
] |
solv-int/9701015 | Koichi Takemura | Kouichi Takemura | The Yangian Symmetry in the Spin Calogero Model and its Applications | 18 pages, AMSLaTeX | null | 10.1088/0305-4470/30/17/025 | RIMS-1126 | solv-int cond-mat hep-th math.QA nlin.SI q-alg | null | By using the non-symmetric Hermite polynomials and a technique based on the
Yangian Gelfand-Zetlin bases, we decompose the space of states of the Calogero
model with spin into irreducible Yangian modules, construct an orthogonal basis
of eigenvectors and derive product-type formulas for norms of these
eigenvectors.
| [
{
"version": "v1",
"created": "Wed, 22 Jan 1997 05:34:38 GMT"
},
{
"version": "v2",
"created": "Tue, 15 Apr 1997 12:32:31 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Takemura",
"Kouichi",
""
]
] |
solv-int/9701016 | Galina A. Korepanova | I.G. Korepanov | Some eigenstates for a model associated with solutions of tetrahedron
equation | 7 pages, LaTeX | null | null | null | solv-int nlin.SI | null | Here we present some eigenstates for a 2+1-dimensional model associated with
a solution of the tetrahedron equation. The eigenstates include those
"particle-like" (namely one-particle and two-particle ones), constructed in
analogy with the usual 1+1-dimensional Bethe ansatz, and some simple
"string-like" ones.
| [
{
"version": "v1",
"created": "Wed, 22 Jan 1997 16:17:03 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Korepanov",
"I. G.",
""
]
] |
solv-int/9701017 | Henrik Aratyn | H. Aratyn, E. Nissimov and S. Pacheva | Method of Squared Eigenfunction Potentials in Integrable Hierarchies of
KP Type | LaTeX, 30pgs, appendix added on binary Darboux-Backlund
transformations | null | 10.1007/s002200050338 | BGU-97/01/Jan-PH, UICHEP-TH/97-1 | solv-int hep-th nlin.SI | null | The method of squared eigenfunction potentials (SEP) is developed
systematically to describe and gain new information about
Kadomtsev-Petviashvili (KP) hierarchy and its reductions. Interrelation to the
tau-function method is discussed in detail. The principal result, which forms
the basis of our SEP method, is the proof that any eigenfunction of the general
KP hierarchy can be represented as a spectral integral over the Baker-Akhiezer
(BA) wave function with a spectral density expressed in terms of SEP. In fact,
the spectral representations of the (adjoint) BA functions can, in turn, be
considered as defining equations for the KP hierarchy. The SEP method is
subsequently used to show how the reduction of the full KP hierarchy to the
constrained KP hierarchies can be given entirely in terms of linear constraint
equations on the pertinent tau-functions. The concept of SEP turns out to be
crucial in providing a description of constrained KP hierarchies in the
language of universal Sato Grassmannian and finding the non-isospectral
Virasoro symmetry generators acting on the underlying tau-functions. The SEP
method is used to write down generalized binary Darboux-Backlund
transformations for constrained KP hierarchies whose orbits are shown to
correspond to a new Toda model on a square lattice. As a result, we obtain a
series of new determinant solutions for the tau-functions generalizing the
known Wronskian (multi-soliton) solutions. Finally, applications to random
matrix models in condensed matter physics are briefly discussed.
| [
{
"version": "v1",
"created": "Fri, 24 Jan 1997 21:06:58 GMT"
},
{
"version": "v2",
"created": "Thu, 27 Mar 1997 14:49:54 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Aratyn",
"H.",
""
],
[
"Nissimov",
"E.",
""
],
[
"Pacheva",
"S.",
""
]
] |
solv-int/9701018 | Kirill Vaninsky | K.L. Vaninsky | Symplectic Structures and Volume Elements in the Function Space for the
Cubic Schrodinger Equation | 20 pages, AMS-TEX | Duke Math. J, vol 92, no. 1, pp. 381-402 (1998) | null | null | solv-int nlin.SI | null | We consider various trace formulas for the cubic Schrodinger equation in the
space of infinitely smooth functions subject to periodic boundary conditions.
The formulas relate conventional integrals of motion to the periods of some
Abelian differentials (holomorphic one-forms) on the spectral curve. We show
that the periods of Abelian differentials are global coordinates on the moduli
space of spectral curves. The exterior derivatives of the holomorphic one-forms
are the basic and higher symplectic structures on the phase space. We write
explicitly these symplectic structures in $QP$ coordinates. We compute the
ratio of two symplectic volume elements in the infinite genus limit.
| [
{
"version": "v1",
"created": "Tue, 28 Jan 1997 01:55:20 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Vaninsky",
"K. L.",
""
]
] |
solv-int/9701019 | Alexander Sorin | A.N. Leznov and A. Sorin | The Solution of the N=2 Supersymmetric f-Toda Chain with Fixed Ends | 15 pages, latex, no figures | Phys.Lett. B402 (1997) 87-100 | 10.1016/S0370-2693(97)00449-8 | JINR E2-97-21 | solv-int hep-th nlin.SI | null | The integrability of the recently introduced N=2 supersymmetric f-Toda chain,
under appropriate boundary conditions, is proven. The recurrent formulae for
its general solutions are derived. As an example, the solution for the simplest
case of boundary conditions is presented in explicit form.
| [
{
"version": "v1",
"created": "Wed, 29 Jan 1997 08:04:00 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Leznov",
"A. N.",
""
],
[
"Sorin",
"A.",
""
]
] |
solv-int/9701020 | Alexander Sorin | A. Sorin | The Discrete Symmetries of the N=2 Supersymmetric GNLS Hierarchies | 8 pages, latex, no figures, report-no added | null | null | JINR E2-97-37 | solv-int hep-th nlin.SI | null | The discrete symmetry transformations of the N=2 supersymmetric (n,m)-GNLS
hierarchy are constructed. Their bosonic limit is analyzed and new discrete
symmetries of the modified GNLS hierarchy are derived. The explicit relations
connecting the integrable hierarchy, produced by the junction of the Lax
operators for the N=2 supersymmetric a=4 KdV and (n-1,m)-GNLS hierarchies, to
the N=2 supersymmetric (n,m)-GNLS hierarchy are established.
| [
{
"version": "v1",
"created": "Wed, 29 Jan 1997 08:30:34 GMT"
},
{
"version": "v2",
"created": "Thu, 13 Feb 1997 07:27:01 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Sorin",
"A.",
""
]
] |
solv-int/9701021 | Marco Ameduri | Marco Ameduri, Costas J. Efthimiou | Is the classical Bukhvostov-Lipatov model integrable? A Painlev\'e
analysis | null | J. Nonlinear Math. Phys. 5 (1998), no. 2, 132-139 | 10.2991/jnmp.1998.5.2.4 | JNMP 4/2002 (Letter) | solv-int hep-th nlin.SI | null | In this work we apply the Weiss, Tabor and Carnevale integrability criterion
(Painlev\'e analysis) to the classical version of the two dimensional
Bukhvostov-Lipatov model. We are led to the conclusion that the model is not
integrable classically, except at a trivial point where the theory can be
described in terms of two uncoupled sine-Gordon models.
| [
{
"version": "v1",
"created": "Wed, 29 Jan 1997 19:49:25 GMT"
},
{
"version": "v2",
"created": "Wed, 1 Apr 1998 00:00:00 GMT"
}
] | 2015-06-26T00:00:00 | [
[
"Ameduri",
"Marco",
""
],
[
"Efthimiou",
"Costas J.",
""
]
] |
solv-int/9701022 | null | Masato Hisakado | Coupled Nonlinear Schr\"{o}dinger equation and Toda equation (the Root
of Integrability) | 11 pages, LateX, to apper in J. Phys. Soc. Jpn. Vol. 66, No 7 | null | 10.1143/JPSJ.66.1939 | null | solv-int hep-th nlin.SI | null | We consider the relation between the discrete coupled nonlinear
Schr\"{o}dinger equation and Toda equation. Introducing complex times we can
show the intergability of the discrete coupled nonlinear Schr\"{o}dinger
equation. In the same way we can show the integrability in coupled case of dark
and bright equations. Using this method we obtain several integrable equations.
| [
{
"version": "v1",
"created": "Fri, 31 Jan 1997 01:00:02 GMT"
},
{
"version": "v2",
"created": "Fri, 11 Apr 1997 06:23:59 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Hisakado",
"Masato",
""
]
] |
solv-int/9702001 | Kenji Kajiwara | Kenji Kajiwara, Kazushi Yamamoto and Yasuhiro Ohta | Rational Solutions for the Discrete Painlev\'e II Equation | 12 pages, latex | null | 10.1016/S0375-9601(97)00397-6 | null | solv-int nlin.SI | null | The rational solutions for the discrete Painlev\'e II equation are
constructed based on the bilinear formalism. It is shown that they are
expressed by the determinant whose entries are given by the Laguerre
polynomials. Continuous limit to the Devisme polynomial representation of the
rational solutions for the Painlev\'e II equation is also discussed.
| [
{
"version": "v1",
"created": "Mon, 10 Feb 1997 04:26:30 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Kajiwara",
"Kenji",
""
],
[
"Yamamoto",
"Kazushi",
""
],
[
"Ohta",
"Yasuhiro",
""
]
] |
solv-int/9702002 | null | Q. P. Liu | Fully Supersymmetric Hierarchies From A Energy Dependent Super Hill
Operator | 15 pages, AMS-LaTex | J. Phys. A: Math. Gen., 30 (1997) 8661 | 10.1088/0305-4470/30/24/025 | null | solv-int hep-th nlin.SI | null | A super Hill operator with energy dependent potentials is proposed and the
associated integrable hierarchy is constructed explicitly. It is shown that in
the general case, the resulted hierarchy is multi-Hamiltonian system. The Miura
type transformations and modified hierarchies are also presented.
| [
{
"version": "v1",
"created": "Thu, 13 Feb 1997 09:47:52 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Liu",
"Q. P.",
""
]
] |
solv-int/9702003 | Juri Suris | Yuri B. Suris (University of Bremen, Germany) | On an integrable discretization of the modified Korteweg-de Vries
equation | 23 pages, LaTeX | Phys. Lett. A, 1997, V.234, p. 91-102. | 10.1016/S0375-9601(97)00592-6 | null | solv-int nlin.SI | null | We find time discretizations for the two ''second flows'' of the
Ablowitz-Ladik hierachy. These discretizations are described by local equations
of motion, as opposed to the previously known ones, due to Taha and Ablowitz.
Certain superpositions of our maps allow a one-field reduction and serve
therefore as valid space-time discretizations of the modified Korteweg-de Vries
equation. We expect the performance of these discretizations to be much better
then that of the Taha-Ablowitz scheme. The way of finding interpolating
Hamiltonians for our maps is also indicated, as well as the solution of an
initial value problem in terms of matrix factorizations.
| [
{
"version": "v1",
"created": "Mon, 17 Feb 1997 11:21:33 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Suris",
"Yuri B.",
"",
"University of Bremen, Germany"
]
] |
solv-int/9702004 | Galina A. Korepanova | I.G. Korepanov | Some eigenstates for a model associated with solutions of tetrahedron
equation. II. A bit of algebraization | LaTeX, 8 pages | null | null | null | solv-int nlin.SI | null | This paper adds two observations to the work solv-int/9701016 where some
eigenstates for a model based on tetrahedron equation have been constructed.
The first observation is that there exists a more "algebraic" construction of
one-particle states, resembling the 1+1-dimensional algebraic Bethe ansatz. The
second observation is that the strings introduced in solv-int/9701016 are
symmetries of a transfer matrix, rather than just eigenstates.
| [
{
"version": "v1",
"created": "Wed, 19 Feb 1997 13:13:03 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Korepanov",
"I. G.",
""
]
] |
solv-int/9702005 | Vadim Vereschagin | V.L.Vereschagin | Asymptotics for Solution to the Cauchy Problem for Volterra Lattice with
Step-Like Initial Values | null | null | null | null | solv-int nlin.SI | null | The connection between modulated Riemann surface of genus one and solution to
Volterra lattice that tends to constants at infinity is studied. The main term
of asymptotics for large time of solution to the mentioned Cauchy problem is
written out.
| [
{
"version": "v1",
"created": "Thu, 20 Feb 1997 05:35:05 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Vereschagin",
"V. L.",
""
]
] |
solv-int/9702006 | G. Tondo | C. Morosi and G. Tondo | Quasi-BiHamiltonian Systems and Separability | 10 pages, AMS-LaTeX 1.1, to appear in J. Phys. A: Math. Gen. (May
1997) | null | 10.1088/0305-4470/30/8/023 | null | solv-int nlin.SI | null | Two quasi--biHamiltonian systems with three and four degrees of freedom are
presented. These systems are shown to be separable in terms of Nijenhuis
coordinates. Moreover the most general Pfaffian quasi-biHamiltonian system with
an arbitrary number of degrees of freedom is constructed (in terms of Nijenhuis
coordinates) and its separability is proved.
| [
{
"version": "v1",
"created": "Mon, 24 Feb 1997 17:34:46 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Morosi",
"C.",
""
],
[
"Tondo",
"G.",
""
]
] |
solv-int/9702007 | Harold Widom | Harold Widom (University of California, Santa Cruz) | An Integral Operator Solution to the Matrix Toda Equations | 8 pages, LaTeX file. An argument improved | J. Int. Eqs. Appl. 10 (1998) 363 | null | null | solv-int funct-an hep-th math.FA nlin.SI | null | In previous work the author found solutions to the Toda equations that were
expressed in terms of determinants of integral operators. Here it is observed
that a simple variant yields solutions to the matrix Toda equations. As an
application another derivation is given of a differential equation of Sato,
Miwa and Jimbo for a particular Fredholm determinant.
| [
{
"version": "v1",
"created": "Wed, 26 Feb 1997 17:45:49 GMT"
},
{
"version": "v2",
"created": "Tue, 6 May 1997 19:01:29 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Widom",
"Harold",
"",
"University of California, Santa Cruz"
]
] |
solv-int/9702008 | null | Unal Goktas and Willy Hereman (Colorado School of Mines) | Symbolic Computation of Conserved Densities for Systems of Nonlinear
Evolution Equations | 31 pages, Latex, uses jsc.sty, submitted to J. Symbolic Computation | null | null | MCS-96-06 | solv-int nlin.SI | null | A new algorithm for the symbolic computation of polynomial conserved
densities for systems of nonlinear evolution equations is presented. The
algorithm is implemented in Mathematica. The program condens.m automatically
carries out the lengthy symbolic computations for the construction of conserved
densities. The code is tested on several well-known partial differential
equations from soliton theory. For systems with parameters, condens.m can be
used to determine the conditions on these parameters so that a sequence of
conserved densities might exist. The existence of a large number of
conservation laws is a predictor for integrability of the system.
| [
{
"version": "v1",
"created": "Thu, 27 Feb 1997 19:58:30 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Goktas",
"Unal",
"",
"Colorado School of Mines"
],
[
"Hereman",
"Willy",
"",
"Colorado School of Mines"
]
] |
solv-int/9703001 | Leonid Dickey | L. A. Dickey | Poisson brackets with divergence terms in field theories: two examples | 7 pages, LaTeX | null | null | null | solv-int nlin.SI | null | In field theories one often works with the functionals which are integrals of
some densities. These densities are defined up to divergence terms (boundary
terms). A Poisson bracket of two functionals is also a functional, i.e., an
integral of a density. Suppose the divergence term in the density of the
Poisson bracket be fixed so that it becomes a bilinear form of densities of two
functionals. Then the left-hand side of the Jacobi identity written in terms of
densities is not necessarily zero but a divergence of a trilinear form. The
question is: what can be said about this trilinear form, what kind of a higher
Jacobi identity (involving four fields) it enjoys? Two examples whose origin is
the theory of integrable systems are given.
| [
{
"version": "v1",
"created": "Sat, 1 Mar 1997 21:23:04 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Dickey",
"L. A.",
""
]
] |
solv-int/9703002 | Sergei Ya. Startsev | S. Ya. Startsev | An analog of the variational derivative and constructive necessary
integrability condition for hyperbolic equation | 6 pages, Latex | null | null | null | solv-int nlin.SI | null | An algorithm is constructed which allows to express conserved flows of
hyperbolic equations in terms of corresponding conserved densities and to
eliminate these flows from conservation laws of hyperbolic equations. The
application of this algorithm to canonical conservation laws gives constructive
necessary integrability conditions of hyperbolic equations in terms of the
generalized Laplace invariants of these equations.
| [
{
"version": "v1",
"created": "Tue, 4 Mar 1997 14:29:17 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Startsev",
"S. Ya.",
""
]
] |
solv-int/9703003 | Mts | V.V. Dmitrieva and R.A. Sharipov | On the point transformations for the second order differential
equations. I | AmSTeX, Version 2.1, 15 pages | null | null | null | solv-int nlin.SI | null | Point transformations for the ordinary differential equations of the form
$y''=P(x,y)+3 Q(x,y) y'+3 R(x,y) (y')^2+S(x,y) (y')^3$ are considered. Some
classical results are resumed. Solution for the equivalence problem for the
equations of general position is described.
| [
{
"version": "v1",
"created": "Thu, 6 Mar 1997 15:17:18 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Dmitrieva",
"V. V.",
""
],
[
"Sharipov",
"R. A.",
""
]
] |
solv-int/9703004 | Juri Suris | Yuri B. Suris (University of Bremen) | A collection of integrable systems of the Toda type in continuous and
discrete time, with 2x2 Lax representations | 33 pp, LaTeX | null | null | null | solv-int nlin.SI | null | A fairly complete list of Toda-like integrable lattice systems, both in the
continuous and discrete time, is given. For each system the Newtonian,
Lagrangian and Hamiltonian formulations are presented, as well as the 2x2 Lax
representation and r-matrix structure. The material is given in the "no
comment" style, in particular, all proofs are omitted.
| [
{
"version": "v1",
"created": "Thu, 6 Mar 1997 17:56:21 GMT"
},
{
"version": "v2",
"created": "Fri, 7 Mar 1997 15:18:14 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Suris",
"Yuri B.",
"",
"University of Bremen"
]
] |
solv-int/9703005 | Andrew Hone | Andrew N.W. Hone | Non-autonomous H\'{e}non-Heiles Systems | 25 pages, Latex. Some minor corrections | null | 10.1016/S0167-2789(98)00010-4 | null | solv-int nlin.SI | null | Scaling similarity solutions of three integrable PDEs, namely the
Sawada-Kotera, fifth order KdV and Kaup-Kupershmidt equations, are considered.
It is shown that the resulting ODEs may be written as non-autonomous
Hamiltonian equations, which are time-dependent generalizations of the
well-known integrable H\'{e}non-Heiles systems. The (time-dependent)
Hamiltonians are given by logarithmic derivatives of the tau-functions
(inherited from the original PDEs). The ODEs for the similarity solutions also
have inherited B\"{a}cklund transformations, which may be used to generate
sequences of rational solutions as well as other special solutions related to
the first Painlev\'{e} transcendent.
| [
{
"version": "v1",
"created": "Wed, 12 Mar 1997 12:55:04 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Hone",
"Andrew N. W.",
""
]
] |
solv-int/9703006 | Manna Miguel | M. A. Manna and V. Merle | Modified Korteweg-de Vries Hierachies in Multiple-Times Variables and
the Solutions of Modified Boussinesq Equations | RevTex file, submitted to Proc. Roy. Soc. London A | null | 10.1098/rspa.1998.0215 | null | solv-int nlin.SI | null | We study solitary-wave and kink-wave solutions of a modified Boussinesq
equation through a multiple-time reductive perturbation method. We use
appropriated modified Korteweg-de Vries hierarchies to eliminate secular
producing terms in each order of the perturbative scheme. We show that the
multiple-time variables needed to obtain a regular perturbative series are
completely determined by the associated linear theory in the case of a
solitary-wave solution, but requires the knowledge of each order of the
perturbative series in the case of a kink-wave solution. These appropriate
multiple-time variables allow us to show that the solitary-wave as well as the
kink-wave solutions of the modified Botussinesq equation are actually
respectively a solitary-wave and a kink-wave satisfying all the equations of
suitable modified Korteweg-de Vries hierarchies.
| [
{
"version": "v1",
"created": "Mon, 10 Mar 1997 08:12:21 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Manna",
"M. A.",
""
],
[
"Merle",
"V.",
""
]
] |
solv-int/9703007 | Leon Jerome | J. Leon and A.V. Mikhailov | Raman Solitons and Raman spikes | RevTex file, 4 pages | null | null | null | solv-int nlin.SI | null | Stimulated Raman scattering of a laser pump pulse seeded by a Stokes pulse
generically leaves a two-level medium initially at rest in an excited state
constituted of static solitons and radiation. The soliton birth manifests as
sudden very large variations of the phase of the output pump pulse. This is
proved by building the IST solution of SRS on the semi-line, which shows
moreover that initial Stokes phase flips induce Raman spikes in the pump output
also for short pulse experiments.
| [
{
"version": "v1",
"created": "Mon, 10 Mar 1997 16:22:20 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Leon",
"J.",
""
],
[
"Mikhailov",
"A. V.",
""
]
] |
solv-int/9703008 | Jarmo Hietarinta | R. Radhakrishnan, M. Lakshmanan, and J. Hietarinta | Inelastic Collision and Switching of Coupled Bright Solitons in Optical
Fibers | 9 pages in LaTeX, 1 PostScript figure. To appear in Phys. Rev. E | null | 10.1103/PhysRevE.56.2213 | null | solv-int nlin.SI | null | By constructing the general six-parameter bright two-soliton solution of the
integrable coupled nonlinear Schrodinger equation (Manakov model) using the
Hirota method, we find that the solitons exhibit certain novel inelastic
collision properties, which have not been observed in any other (1+1)
dimensional soliton system so far. In particular, we identify the exciting
possibility of switching solitons between modes by changing the phase. However,
the standard elastic collision property of solitons is regained with specific
choices of parameters.
| [
{
"version": "v1",
"created": "Wed, 12 Mar 1997 11:24:38 GMT"
},
{
"version": "v2",
"created": "Mon, 30 Jun 1997 08:17:44 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Radhakrishnan",
"R.",
""
],
[
"Lakshmanan",
"M.",
""
],
[
"Hietarinta",
"J.",
""
]
] |
solv-int/9703009 | Jose Geraldo Pereira | R. A. Kraenkel, J. G. Pereira and E. C. de Rey Neto (IFT-UNESP, Sao
Paulo, Brazil) | Linearizability of the Perturbed Burgers Equation | 10 pages, RevTeX, no figures | null | 10.1103/PhysRevE.58.2526 | IFT-P.020/97 | solv-int nlin.SI | null | We show in this letter that the perturbed Burgers equation $u_t = 2uu_x +
u_{xx} + \epsilon ( 3 \alpha_1 u^2 u_x + 3\alpha_2 uu_{xx} + 3\alpha_3 u_x^2 +
\alpha_4 u_{xxx} )$ is equivalent, through a near-identity transformation and
up to order \epsilon, to a linearizable equation if the condition $3\alpha_1 -
3\alpha_3 - 3/2 \alpha_2 + 3/2 \alpha_4 = 0$ is satisfied. In the case this
condition is not fulfilled, a normal form for the equation under consideration
is given. Then, to illustrate our results, we make a linearizability analysis
of the equations governing the dynamics of a one-dimensional gas.
| [
{
"version": "v1",
"created": "Wed, 19 Mar 1997 14:38:15 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Kraenkel",
"R. A.",
"",
"IFT-UNESP, Sao\n Paulo, Brazil"
],
[
"Pereira",
"J. G.",
"",
"IFT-UNESP, Sao\n Paulo, Brazil"
],
[
"Neto",
"E. C. de Rey",
"",
"IFT-UNESP, Sao\n Paulo, Brazil"
]
] |
solv-int/9703010 | Galina A. Korepanova | I.G. Korepanov | Some eigenstates for a model associated with solutions of tetrahedron
equation. III. Tetrahedral Zamolodchikov algebras and perturbed strings | LaTeX, 7 pages | null | null | null | solv-int nlin.SI | null | This paper continues the series begun with works solv-int/9701016 and
solv-int/9702004. Here we show how to construct eigenstates for a model based
on tetrahedron equation using the tetrahedral Zamolodchikov algebras. This
yields, in particular, new eigenstates for the model on infinite lattice --
`perturbed', or `broken', strings.
| [
{
"version": "v1",
"created": "Thu, 20 Mar 1997 14:12:36 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Korepanov",
"I. G.",
""
]
] |
solv-int/9703011 | Andres Gomberoff | Andres Gomberoff and Sergio A. Hojman | Non-standard Construction of Hamiltonian Structures | 13 pages, Revtex | J.Phys.A30:5077-5084,1997 | 10.1088/0305-4470/30/14/018 | null | solv-int hep-th nlin.SI | null | Examples of the construction of Hamiltonian structures for dynamical systems
in field theory (including one reputedly non-Hamiltonian problem) without using
Lagrangians, are presented. The recently developed method used requires the
knowledge of one constant of the motion of the system under consideration and
one solution of the symmetry equation.
| [
{
"version": "v1",
"created": "Thu, 20 Mar 1997 23:38:36 GMT"
}
] | 2008-11-26T00:00:00 | [
[
"Gomberoff",
"Andres",
""
],
[
"Hojman",
"Sergio A.",
""
]
] |
solv-int/9703012 | Hasan Gumral | H. Gumral | Lagrangian Description, Symplectic Structure, and Invariants of 3D Fluid
Flow | Plain Latex, 15 pages | null | 10.1016/S0375-9601(97)00404-0 | RIBS-PH-5/97 | solv-int nlin.SI | null | Three dimensional unsteady flow of fluids in the Lagrangian description is
considered as an autonomous dynamical system in four dimensions. The condition
for the existence of a symplectic structure on the extended space is the frozen
field equations of the Eulerian description of motion. Integral invariants of
symplectic flow are related to conservation laws of the dynamical equation. A
scheme generating infinite families of symmetries and invariants is presented.
For the Euler equations these invariants are shown to have a geometric origin
in the description of flow as geodesic motion; they are also interpreted in
connection with the particle relabelling symmetry.
| [
{
"version": "v1",
"created": "Mon, 24 Mar 1997 10:08:50 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Gumral",
"H.",
""
]
] |
solv-int/9703013 | Robert Carroll | Robert Carroll (Mathematics Dept., University of Illinois, Urbana, IL) | WDVV and DZM | Latex, 14 pages | null | 10.1016/S0375-9601(97)00588-4 | null | solv-int nlin.SI | null | We show how the WDVV equations and the DZM system can be characterized via a
background family of functions.
| [
{
"version": "v1",
"created": "Tue, 25 Mar 1997 07:49:18 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Carroll",
"Robert",
"",
"Mathematics Dept., University of Illinois, Urbana, IL"
]
] |
solv-int/9704001 | Andrei Mironov | A.Zabrodin | A survey of Hirota's difference equations | LaTeX, 43 pages, LaTeX figures (with emlines2.sty) | null | 10.1007/BF02634165 | ITEP/TH-10/97 | solv-int hep-th nlin.SI | null | A review of selected topics in Hirota's bilinear difference equation (HBDE)
is given. This famous 3-dimensional difference equation is known to provide a
canonical integrable discretization for most important types of soliton
equations. Similarly to the continuous theory, HBDE is a member of an infinite
hierarchy. The central point of our exposition is a discrete version of the
zero curvature condition explicitly written in the form of discrete
Zakharov-Shabat equations for M-operators realized as difference or
pseudo-difference operators. A unified approach to various types of M-operators
and zero curvature representations is suggested. Different reductions of HBDE
to 2-dimensional equations are considered. Among them discrete counterparts of
the KdV, sine-Gordon, Toda chain, relativistic Toda chain and other typical
examples are discussed in detail.
| [
{
"version": "v1",
"created": "Sun, 30 Mar 1997 17:10:51 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Zabrodin",
"A.",
""
]
] |
solv-int/9704002 | Laszlo Feher | Laszlo Feher, Ian Marshall | Extended matrix Gelfand-Dickey hierarchies: reduction to classical Lie
algebras | plain TeX, 12 pages | null | 10.1088/0305-4470/30/16/022 | null | solv-int hep-th nlin.SI | null | The Drinfeld-Sokolov reduction method has been used to associate with $gl_n$
extensions of the matrix r-KdV system. Reductions of these systems to the fixed
point sets of involutive Poisson maps, implementing reduction of $gl_n$ to
classical Lie algebras of type $B, C, D$, are here presented. Modifications
corresponding, in the first place to factorisation of the Lax operator, and
then to Wakimoto realisations of the current algebra components of the
factorisation, are also described.
| [
{
"version": "v1",
"created": "Mon, 31 Mar 1997 12:58:03 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Feher",
"Laszlo",
""
],
[
"Marshall",
"Ian",
""
]
] |
solv-int/9704003 | null | G. Cicogna | Convergent Normal Forms of Symmetric Dynamical Systems | 11 pag., Plain TeX | null | 10.1088/0305-4470/30/17/013 | null | solv-int nlin.SI | null | It is shown that the presence of Lie-point-symmetries of (non-Hamiltonian)
dynamical systems can ensure the convergence of the coordinate transformations
which take the dynamical sytem (or vector field) into Poincar\'e-Dulac normal
form.
| [
{
"version": "v1",
"created": "Wed, 2 Apr 1997 07:23:21 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Cicogna",
"G.",
""
]
] |
solv-int/9704004 | Kanehisa Takasaki | Kanehisa Takasaki (Kyoto University) | Spectral Curves and Whitham Equations in Isomonodromic Problems of
Schlesinger Type | 41 pages, latex, no figures; typos in references are corrected | Asian J.Math. 4 (2) (1998), 1049-1078 | null | KUCP-0105 | solv-int hep-th math.QA nlin.SI q-alg | null | It has been known since the beginning of this century that isomonodromic
problems --- typically the Painlev\'e transcendents --- in a suitable
asymptotic region look like a kind of ``modulation'' of isospectral problem.
This connection between isomonodromic and isospectral problems is reconsidered
here in the light of recent studies related to the Seiberg-Witten solutions of
$N = 2$ supersymmetric gauge theories. A general machinary is illustrated in a
typical isomonodromic problem, namely the Schlesinger equation, which is
reformulated to include a small parameter $\epsilon$. In the small-$\epsilon$
limit, solutions of this isomonodromic problem are expected to behave as a
slowly modulated finite-gap solution of an isospectral problem. The modulation
is caused by slow deformations of the spectral curve of the finite-gap
solution. A modulation equation of this slow dynamics is derived by a heuristic
method. An inverse period map of Seiberg-Witten type turns out to give general
solutions of this modulation equation. This construction of general solution
also reveals the existence of deformations of Seiberg-Witten type on the same
moduli space of spectral curves. A prepotential is also constructed in the same
way as the prepotential of the Seiberg-Witten theory.
| [
{
"version": "v1",
"created": "Tue, 8 Apr 1997 02:21:28 GMT"
},
{
"version": "v2",
"created": "Fri, 17 Oct 1997 08:55:32 GMT"
},
{
"version": "v3",
"created": "Fri, 7 Nov 1997 09:03:51 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Takasaki",
"Kanehisa",
"",
"Kyoto University"
]
] |
solv-int/9704005 | Guest | R. Myrzakulov (High Energy Physics Institute, National Academy of
Sciences, Alma-Ata, Kazakstan), S. Vijayalakshmi, G. N. Nugmanova, and M.
Lakshmanan (Centre for Nonlinear Dynamics, Department of Physics,
Bharathidasan University, Tiruchirapalli, India) | A (2+1) dimensional integrable spin model: Geometrical and gauge
equivalent counterpart, solitons and localized coherent structures | 14 pages, LaTex, no figures; email of first author:
[email protected] and [email protected] | Physics Letters A, v.233, N4-6, 391-396 (1997) | 10.1016/S0375-9601(97)00457-X | null | solv-int nlin.SI | null | A non-isospectral (2+1) dimensional integrable spin equation is investigated.
It is shown that its geometrical and gauge equivalent counterparts is the (2+1)
dimensional nonlinear Schr\"odinger equation introduced by Zakharov and studied
recently by Strachan. Using a Hirota bilinearised form, line and curved soliton
solutions are obtained. Using certain freedom (arbitrariness) in the solutions
of the bilinearised equation, exponentially localized dromion-like solutions
for the potential is found. Also, breaking soliton solutions (for the spin
variables) of the shock wave type and algebraically localized nature are
constructed.
| [
{
"version": "v1",
"created": "Sun, 6 Apr 1997 06:45:34 GMT"
}
] | 2013-10-15T00:00:00 | [
[
"Myrzakulov",
"R.",
"",
"High Energy Physics Institute, National Academy of\n Sciences, Alma-Ata, Kazakstan"
],
[
"Vijayalakshmi",
"S.",
"",
"Centre for Nonlinear Dynamics, Department of Physics,\n Bharathidasan University, Tiruchirapalli, India"
],
[
"Nugmanova",
"G. N.",
"",
"Centre for Nonlinear Dynamics, Department of Physics,\n Bharathidasan University, Tiruchirapalli, India"
],
[
"Lakshmanan",
"M.",
"",
"Centre for Nonlinear Dynamics, Department of Physics,\n Bharathidasan University, Tiruchirapalli, India"
]
] |
solv-int/9704006 | Hisao Konuma | Satoru Saito, Noriko Saitoh, Hisao Konuma and Katsuhiko Yoshida | Complex Analysis of a Piece of Toda Lattice | 17 pages, LaTeX | null | 10.1088/0305-4470/30/19/029 | null | solv-int hep-th nlin.SI | null | We study a small piece of two dimensional Toda lattice as a complex dynamical
system. In particular the Julia set, which appears when the piece is deformed,
is shown analytically how it disappears as the system approaches to the
integrable limit.
| [
{
"version": "v1",
"created": "Sat, 5 Apr 1997 12:32:41 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Saito",
"Satoru",
""
],
[
"Saitoh",
"Noriko",
""
],
[
"Konuma",
"Hisao",
""
],
[
"Yoshida",
"Katsuhiko",
""
]
] |
solv-int/9704007 | Hisao Konuma | Satoru Saito | The Correspondence between Discrete Surface and Difference Geometry of
the KP-hierarchy | null | null | null | null | solv-int hep-th nlin.SI | null | The correspondence between two geometrical descriptions of the KP-hierarchy,
one by discrete surface and another by difference analogue of differential
geometry, is given.
| [
{
"version": "v1",
"created": "Sun, 6 Apr 1997 06:08:17 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Saito",
"Satoru",
""
]
] |
solv-int/9704008 | Hisao Konuma | Satoru Saito | Dual Resonance Model Solves the Yang-Baxter Equation | 10 pages, LaTeX | null | 10.1088/0305-4470/30/23/025 | null | solv-int hep-th nlin.SI | null | The duality of dual resonance models is shown to imply that the four point
string correlation function solves the Yang-Baxter equation. A reduction of
transfer matrices to $A_l$ symmetry is described by a restriction of the KP
$\tau$ function to Toda molecules.
| [
{
"version": "v1",
"created": "Sun, 6 Apr 1997 06:18:36 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Saito",
"Satoru",
""
]
] |
solv-int/9704009 | Ken Umeno | Ken Umeno | Singularity analysis towards nonintegrability of nonhomogeneous
nonlinear lattices | Latex 6pages, use crckapb.sty | Hamiltonian Systems with Three or More Degrees of Freedom, Edited
by C. Simo, pp.614-617 (Kluwer,1999). | null | null | solv-int nlin.SI | null | We show non-integrability of the nonlinear lattice of Fermi-Pasta-Ulam type
via the singularity analysis(Picard-Vessiot theory) of normal variational
equations of Lam\'e type.
| [
{
"version": "v1",
"created": "Wed, 16 Apr 1997 10:08:39 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Umeno",
"Ken",
""
]
] |
solv-int/9704010 | Gregorio Falqui | Gregorio Falqui, Cesare Reina, and Alessandro Zampa | Krichever Maps, Faa' di Bruno Polynomials, and Cohomology in KP Theory | 16 pages, LaTex using amssymb.sty. To be published in Lett. Math.
Phys | null | null | SISSA/ISAS/37/97/FM | solv-int nlin.SI | null | We study the geometrical meaning of the Faa' di Bruno polynomials in the
context of KP theory. They provide a basis in a subspace W of the universal
Grassmannian associated to the KP hierarchy. When W comes from geometrical data
via the Krichever map, the Faa' di Bruno recursion relation turns out to be the
cocycle condition for (the Welters hypercohomology group describing) the
deformations of the dynamical line bundle on the spectral curve together with
the meromorphic sections which give rise to the Krichever map. Starting from
this, one sees that the whole KP hierarchy has a similar cohomological meaning.
| [
{
"version": "v1",
"created": "Tue, 15 Apr 1997 08:49:37 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Falqui",
"Gregorio",
""
],
[
"Reina",
"Cesare",
""
],
[
"Zampa",
"Alessandro",
""
]
] |
solv-int/9704011 | Michael Shapiro | M.Gekhtman and M. Shapiro | Non-commutative and commutative integrability of generic Toda flows in
simple Lie algebras | AMSTeX, 24 pages, no figures, available via
http://www.math.kth.se/~mshapiro/ | null | null | null | solv-int nlin.SI | null | In this paper we prove the complete integrability of Toda flows on generic
coadjoint orbits in simple Lie algebras.
| [
{
"version": "v1",
"created": "Thu, 17 Apr 1997 16:48:46 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Gekhtman",
"M.",
""
],
[
"Shapiro",
"M.",
""
]
] |
solv-int/9704012 | Igor Loutsenko | Y. Berest, I. Loutsenko | Huygens' Principle in Minkowski Spaces and Soliton Solutions of the
Korteweg-de Vries Equation | 23 pages, LaTeX, to be published in Comm.Math.Phys (1997) | null | 10.1007/s002200050235 | null | solv-int nlin.SI | null | A new class of linear second order hyperbolic partial differential operators
satisfying Huygens' principle in Minkowski spaces is presented. The
construction reveals a direct connection between Huygens' principle and the
theory of solitary wave solutions of the Korteweg-de Vries equation.
| [
{
"version": "v1",
"created": "Fri, 18 Apr 1997 22:00:52 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Berest",
"Y.",
""
],
[
"Loutsenko",
"I.",
""
]
] |
solv-int/9704013 | Galina A. Korepanova | I.G. Korepanov | Some eigenstates for a model associated with solutions of tetrahedron
equation. IV. String-particle marriage | LaTeX, 6 pages | null | null | null | solv-int nlin.SI | null | This paper continues the series begun with works solv-int/9701016,
solv-int/9702004 and solv-int/9703010. Here we construct more sophisticated
strings, combining ideas from those papers and some considerations involving
solutions of tetrahedron equation due to Sergeev, Mangazeev and Stroganov.
| [
{
"version": "v1",
"created": "Sat, 19 Apr 1997 08:40:04 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Korepanov",
"I. G.",
""
]
] |
solv-int/9704014 | Kaptsov | O. V. Kaptsov, Yu. V. Shan'ko (Computing Center, Academy of Sciences,
Krasnoyarsk, Russia) | Trilinear representation and the Moutard transformation for the
Tzitzeica equation | 16 pages (30 Kbytes), standard LaTeX 2.09, run twice to get the right
cross-references | null | null | null | solv-int nlin.SI | null | In the paper we present a trilinear form and a Darboux-type transformation to
an equation considered by Tzitzeica in 1910. This equation equivalent to the
Bullough-Dodd-Jiber-Shabat equation. Soliton solutions are constructed by
dressing the trivial solution.
| [
{
"version": "v1",
"created": "Mon, 21 Apr 1997 12:43:57 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Kaptsov",
"O. V.",
"",
"Computing Center, Academy of Sciences,\n Krasnoyarsk, Russia"
],
[
"Shan'ko",
"Yu. V.",
"",
"Computing Center, Academy of Sciences,\n Krasnoyarsk, Russia"
]
] |
solv-int/9704015 | Ovidiu Lipan | O. Lipan, P.B. Wiegmann and A. Zabrodin | Fusion rules for Quantum Transfer Matrices as a Dynamical System on
Grassmann Manifolds | LaTex (MPLA macros included) 10 pages, 1 figure, included in the text | Mod.Phys.Lett. A12 (1997) 1369-1378 | 10.1142/S0217732397001394 | null | solv-int hep-th math.QA nlin.SI q-alg | null | We show that the set of transfer matrices of an arbitrary fusion type for an
integrable quantum model obey these bilinear functional relations, which are
identified with an integrable dynamical system on a Grassmann manifold (higher
Hirota equation). The bilinear relations were previously known for a particular
class of transfer matrices corresponding to rectangular Young diagrams. We
extend this result for general Young diagrams. A general solution of the
bilinear equations is presented.
| [
{
"version": "v1",
"created": "Tue, 22 Apr 1997 23:50:29 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Lipan",
"O.",
""
],
[
"Wiegmann",
"P. B.",
""
],
[
"Zabrodin",
"A.",
""
]
] |
solv-int/9704016 | null | Unal Goktas, Willy Hereman, Grant Erdmann (Colorado School of Mines) | Computation of conserved densities for systems of nonlinear
differential-difference equations | submitted to Phys. Lett A, 10 pages, latex | null | 10.1016/S0375-9601(97)00750-0 | MCS-97-02 | solv-int nlin.SI | null | A new method for the computation of conserved densities of nonlinear
differential-difference equations is applied to Toda lattices and
discretizations of the Korteweg-de Vries and nonlinear Schrodinger equations.
The algorithm, which can be implemented in computer algebra languages such as
Mathematica, can be used as an indicator of integrability.
| [
{
"version": "v1",
"created": "Wed, 23 Apr 1997 22:46:31 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Goktas",
"Unal",
"",
"Colorado School of Mines"
],
[
"Hereman",
"Willy",
"",
"Colorado School of Mines"
],
[
"Erdmann",
"Grant",
"",
"Colorado School of Mines"
]
] |
solv-int/9705001 | Loriano Bonora | L.Bonora, S.Krivonos | Hamiltonian structure and coset construction of the supersymmetric
extensions of N=2 KdV hierarchy | 11 pages, Latex, a few modifications in the text | null | 10.1142/S0217732397003162 | SISSA 59/97/EP | solv-int hep-th nlin.SI | null | A manifestly N=2 supersymmetric coset formalism is applied to analyse the
"fermionic" extensions of N=2 $a=4$ and $a=-2$ KdV hierarchies. Both these
hierarchies can be obtained from a manifest N=2 coset construction. This coset
is defined as the quotient of some local but non-linear superalgebra by a
$\hat{U(1)}$ subalgebra. Three superextensions of N=2 KdV hierarchy are
proposed, among which one seems to be entirely new.
| [
{
"version": "v1",
"created": "Tue, 29 Apr 1997 18:30:44 GMT"
},
{
"version": "v2",
"created": "Tue, 6 May 1997 11:35:12 GMT"
},
{
"version": "v3",
"created": "Tue, 8 Jul 1997 07:54:37 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Bonora",
"L.",
""
],
[
"Krivonos",
"S.",
""
]
] |
solv-int/9705002 | Jarmo Hietarinta | Jarmo Hietarinta and Kenji Kajiwara | Rational solutions to d-PIV | 11 pages, LaTeX2e with epic. To appear in the proceedings of SIDE II,
Canterbury 1996 | null | null | null | solv-int nlin.SI | null | We study the rational solutions of the discrete version of Painleve's fourth
equation d-PIV. The solutions are generated by applying Schlesinger
transformations on the seed solutions -2z and -1/z. After studying the
structure of these solutions we are able to write them in a determinantal form
that includes an interesting parameter shift that vanishes in the continuous
limit.
| [
{
"version": "v1",
"created": "Thu, 1 May 1997 10:54:16 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Hietarinta",
"Jarmo",
""
],
[
"Kajiwara",
"Kenji",
""
]
] |
solv-int/9705003 | null | V.S. Dryuma, B.G. Konopelchenko | On equation of geodesic deviation and its solutions | 17 pages, Latex | Bulletin of Moldavian Academy of Sciences, ser. math. N3, (1996)
31-48 | null | null | solv-int nlin.SI | null | Equations of geodesic deviation for the 3-dimensional and 4-dimensional
Riemann spaces are discussed. Availability of wide classes of exact solutions
of such equations, due to recent results for the matrix Schr\"odinger equation,
is demonstrated. Particular classes of exact solutions for the geodesic
deviation equation as well as for the Raychaudhuri and generalized Raychaudhuri
equation are presented. Solutions of geodesic deviation equation for the
Schwarzshild and Kasner metrics are found.
| [
{
"version": "v1",
"created": "Fri, 2 May 1997 14:18:07 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Dryuma",
"V. S.",
""
],
[
"Konopelchenko",
"B. G.",
""
]
] |
solv-int/9705004 | Andrey V. Tsiganov | A.V. Tsiganov | On superintegrable systems closed to geodesic motion | 22 pages, LaTeX | null | null | null | solv-int nlin.SI | null | In this work we consider superintegrable systems in the classical $r$-matrix
method. By using other authomorphisms of the loop algebras we construct new
superintegrable systems with rational potentials from geodesic motion on
$R^{2n}$.
| [
{
"version": "v1",
"created": "Tue, 6 May 1997 07:42:40 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Tsiganov",
"A. V.",
""
]
] |
solv-int/9705005 | Galina A. Korepanova | I.G. Korepanov | Some eigenstates for a model associated with solutions of tetrahedron
equation. V. Two cases of string superposition | LaTeX, 7 pages | null | null | null | solv-int nlin.SI | null | In paper IV (solv-int/9704013) we have considered a string living in the
infinite lattice that was, in a sense, generated by a "particle". Here we show
how to construct multi-string eigenstates generated by several particles. It
turns out that, at least in some cases, this allows us to bypass the
difficulties of constructing multi-particle states. We also present and discuss
the "dispersion relations" for our particles-strings.
| [
{
"version": "v1",
"created": "Tue, 6 May 1997 08:05:11 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Korepanov",
"I. G.",
""
]
] |
solv-int/9705006 | Dr. L. Bordag | L.A. Bordag (Leipzig) and V.S. Dryuma (Kishinev) | Investigation of dynamical systems using tools of the theory of
invariants and projective geometry | 18 pages, Latex, to appear in J. of Applied Mathematics (ZAMP) | null | 10.1007/s000330050061 | NTZ-Preprint 24/95, Leipzig, 1995 | solv-int chao-dyn nlin.CD nlin.SI | null | The investigation of nonlinear dynamical systems of the type
$\dot{x}=P(x,y,z),\dot{y}=Q(x,y,z),\dot{z}=R(x,y,z)$ by means of reduction to
some ordinary differential equations of the second order in the form
$y''+a_1(x,y)y'^3+3a_2(x,y)y'^2+3a_3(x,y)y'+a_4(x,y)=0$ is done. The main
backbone of this investigation was provided by the theory of invariants
developed by S. Lie, R. Liouville and A. Tresse at the end of the 19th century
and the projective geometry of E. Cartan. In our work two, in some sense
supplementary, systems are considered: the Lorenz system $\dot{x}=\sigma (y-x),
\dot{y}=rx-y-zx,\dot{z}=xy-bz $ and the R\"o\ss ler system
$\dot{x}=-y-z,\dot{y}=x+ay,\dot{z}=b+xz-cz.$. The invarinats for the ordinary
differential equations, which correspond to the systems mentioned abouve, are
evaluated. The connection of values of the invariants with characteristics of
dynamical systems is established.
| [
{
"version": "v1",
"created": "Wed, 7 May 1997 21:34:13 GMT"
}
] | 2018-08-29T00:00:00 | [
[
"Bordag",
"L. A.",
"",
"Leipzig"
],
[
"Dryuma",
"V. S.",
"",
"Kishinev"
]
] |
solv-int/9705007 | Basile Grammaticos | Stephane Lafortune, Basil Grammaticos, Alfred Ramani | Constructing Integrable Third Order Systems:The Gambier Approach | 14 pages, TEX FILE | Inverse Problems 14, 287-298 (1998) | 10.1088/0266-5611/14/2/005 | null | solv-int nlin.SI | null | We present a systematic construction of integrable third order systems based
on the coupling of an integrable second order equation and a Riccati equation.
This approach is the extension of the Gambier method that led to the equation
that bears his name. Our study is carried through for both continuous and
discrete systems. In both cases the investigation is based on the study of the
singularities of the system (the Painlev\'e method for ODE's and the
singularity confinement method for mappings).
| [
{
"version": "v1",
"created": "Mon, 12 May 1997 15:57:40 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Lafortune",
"Stephane",
""
],
[
"Grammaticos",
"Basil",
""
],
[
"Ramani",
"Alfred",
""
]
] |
solv-int/9705008 | Dita Petre | Petre Dita and Nicolae Grama | On Adomian's Decomposition Method for Solving Differential Equations | 11 pages, Latex, no figure | null | null | null | solv-int nlin.SI | null | We show that with a few modifications the Adomian's method for solving second
order differential equations can be used to obtain the known results of the
special functions of mathematical physics. The modifications are necessary in
order to take correctly into account the behaviour of the solutions in the
neighborhood of the singular points.
| [
{
"version": "v1",
"created": "Wed, 14 May 1997 10:35:16 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Dita",
"Petre",
""
],
[
"Grama",
"Nicolae",
""
]
] |
solv-int/9705009 | Leonid Bogdanov | L.V. Bogdanov (IINS, L.D. Landau ITP, Moscow) and B.G. Konopelchenko
(Universita di Lecce, Italy) | Analytic-bilinear approach to integrable hierarchies. II. Multicomponent
KP and 2D Toda lattice hierarchies | 43 pages, Latex | null | 10.1063/1.532531 | null | solv-int nlin.SI | null | Analytic-bilinear approach for construction and study of integrable
hierarchies is discussed. Generalized multicomponent KP and 2D Toda lattice
hierarchies are considered. This approach allows to represent generalized
hierarchies of integrable equations in a condensed form of finite functional
equations. Generalized hierarchy incorporates basic hierarchy, modified
hierarchy, singularity manifold equation hierarchy and corresponding linear
problems. Different levels of generalized hierarchy are connected via
invariants of Combescure symmetry transformation. Resolution of functional
equations also leads to the $\tau $-function and addition formulae to it.
| [
{
"version": "v1",
"created": "Fri, 16 May 1997 00:35:27 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Bogdanov",
"L. V.",
"",
"IINS, L.D. Landau ITP, Moscow"
],
[
"Konopelchenko",
"B. G.",
"",
"Universita di Lecce, Italy"
]
] |
solv-int/9705010 | Renat Zhdanov | Renat Zhdanov (Institute of Mathematics, Kyiv.) | Integrability of Riccati equations and the stationary KdV equations | 6 pages, LaTeX | null | null | null | solv-int nlin.SI | null | Using the S.Lie's infinitesimal approach we establish the connection between
integrability of a one-parameter family of the Riccati equations and the
stationary KdV hierarchy.
| [
{
"version": "v1",
"created": "Sat, 17 May 1997 16:43:22 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Zhdanov",
"Renat",
"",
"Institute of Mathematics, Kyiv."
]
] |
solv-int/9705011 | Renat Zhdanov | Renat Zhdanov, Ihor Revenko and Wilhelm Fushchych (Institute of
Mathematics, Kyiv) | Stationary mKdV hierarchy and integrability of the Dirac equations by
quadratures | 6 pages, LaTeX | null | 10.1016/S0375-9601(98)00114-5 | null | solv-int nlin.SI | null | Using the Lie's infinitesimal method we establish that the Dirac equation in
one variable is integrable by quadratures if the potential V(x) is a solution
of one of the equations of the stationary mKdV hierarchy.
| [
{
"version": "v1",
"created": "Sat, 17 May 1997 16:45:15 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Zhdanov",
"Renat",
"",
"Institute of\n Mathematics, Kyiv"
],
[
"Revenko",
"Ihor",
"",
"Institute of\n Mathematics, Kyiv"
],
[
"Fushchych",
"Wilhelm",
"",
"Institute of\n Mathematics, Kyiv"
]
] |
solv-int/9705012 | null | Q. P. Liu and M. Manas | Vectorial Darboux Transformations for the Kadomtsev-Petviashvili
Hierarchy | 26 pages, some formulae corrected. To appear in J. Nonlin. Sci | null | null | null | solv-int hep-th nlin.SI | null | We consider the vectorial approach to the binary Darboux transformations for
the Kadomtsev-Petviashvili hierarchy in its Zakharov-Shabat formulation. We
obtain explicit formulae for the Darboux transformed potentials in terms of
Grammian type determinants. We also study the $n$-th Gel'fand-Dickey hierarchy
introducing spectral operators and obtaining similar results. We reduce the
above mentioned results to the Kadomtsev-Petviashvili I and II real forms,
obtaining corresponding vectorial Darboux transformations. In particular for
the Kadomtsev-Petviashvili I hierarchy we get the line soliton, the lump
solution and the Johnson-Thompson lump, and the corresponding determinant
formulae for the non-linear superposition of several of them. For
Kadomtsev-Petviashvili II apart from the line solitons we get singular rational
solutions with its singularity set describing the motion of strings in the
plane. We also consider the I and II real forms for the Gel'fand-Dickey
hierarchies obtaining the vectorial Darboux transformation in both cases.
| [
{
"version": "v1",
"created": "Wed, 21 May 1997 18:22:09 GMT"
},
{
"version": "v2",
"created": "Tue, 26 May 1998 09:33:14 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Liu",
"Q. P.",
""
],
[
"Manas",
"M.",
""
]
] |
solv-int/9705013 | Kanehisa Takasaki | Partha Guha and Kanehisa Takasaki | Dispersionless Hierarchies, Hamilton-Jacobi Theory and Twistor
Correspondences | 20 pages, latex, no figures | J. Geom. Phys. 25 (3-4) (1998), 326-340 | 10.1016/S0393-0440(97)00034-X | RIMS-1124 | solv-int hep-th nlin.SI | null | The dispersionless KP and Toda hierarchies possess an underlying twistorial
structure. A twistorial approach is partly implemented by the method of
Riemann-Hilbert problem. This is however still short of clarifying geometric
ingredients of twistor theory, such as twistor lines and twistor surfaces. A
more geometric approach can be developed in a Hamilton-Jacobi formalism of
Gibbons and Kodama. AMS Subject Classifiation (1991): 35Q20, 58F07,70H99
| [
{
"version": "v1",
"created": "Thu, 22 May 1997 03:46:17 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Guha",
"Partha",
""
],
[
"Takasaki",
"Kanehisa",
""
]
] |
solv-int/9705014 | Wen-Xiu Ma | W. X. Ma, R. K. Bullough, P. J. Caudrey and W. I. Fushchych | Time-Dependent Symmetries of Variable-Coefficient Evolution Equations
and Graded Lie Algebras | 11 pages, latex, to appear in J. Phys. A: Math. Gen | null | 10.1088/0305-4470/30/14/023 | null | solv-int nlin.SI | null | Polynomial-in-time dependent symmetries are analysed for polynomial-in-time
dependent evolution equations. Graded Lie algebras, especially Virasoro
algebras, are used to construct nonlinear variable-coefficient evolution
equations, both in 1+1 dimensions and in 2+1 dimensions, which possess
higher-degree polynomial-in-time dependent symmetries. The theory also provides
a kind of new realisation of graded Lie algebras. Some illustrative examples
are given.
| [
{
"version": "v1",
"created": "Tue, 27 May 1997 08:51:25 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Ma",
"W. X.",
""
],
[
"Bullough",
"R. K.",
""
],
[
"Caudrey",
"P. J.",
""
],
[
"Fushchych",
"W. I.",
""
]
] |
solv-int/9705015 | Wen-Xiu Ma | W. X. Ma, R. K. Bullough and P. J. Caudrey | Graded Symmetry Algebras of Time-Dependent Evolution Equations and
Application to the Modified KP equations | 19 pages, latex, to appear in J. Nonlinear Math. Phys | null | 10.2991/jnmp.1997.4.3-4.6 | null | solv-int nlin.SI | null | By starting from known graded Lie algebras, including Virasoro algebras, new
kinds of time-dependent evolution equations are found possessing graded
symmetry algebras. The modified KP equations are taken as an illustrative
example: new modified KP equations with $m$ arbitrary time-dependent
coefficients are obtained possessing symmetries involving $m$ arbitrary
functions of time. A particular graded symmetry algebra for the modified KP
equations is derived in this connection homomorphic to the Virasoro algebras.
| [
{
"version": "v1",
"created": "Tue, 27 May 1997 08:52:10 GMT"
}
] | 2015-06-26T00:00:00 | [
[
"Ma",
"W. X.",
""
],
[
"Bullough",
"R. K.",
""
],
[
"Caudrey",
"P. J.",
""
]
] |
solv-int/9705016 | Kanehisa Takasaki | Kanehisa Takasaki | Dual Isomonodromic Problems and Whitham Equations | 15 pages, latex, no figures. Several sentences are added in order to
clarify the contents of Sections 5 and 6 | Lett.Math.Phys. 43 (1998) 123-135 | null | KUCP-0106 | solv-int hep-th math.QA nlin.SI q-alg | null | The author's recent results on an asymptotic description of the Schlesinger
equation are generalized to the JMMS equation. As in the case of the
Schlesinger equation, the JMMS equation is reformulated to include a small
parameter $\epsilon$. By the method of multiscale analysis, the isomonodromic
problem is approximated by slow modulations of an isospectral problem. A
modulation equation of this slow dynamics is proposed, and shown to possess a
number of properties similar to the Seiberg- Witten solutions of low energy
supersymmetric gauge theories.
| [
{
"version": "v1",
"created": "Wed, 28 May 1997 08:14:13 GMT"
},
{
"version": "v2",
"created": "Mon, 16 Jun 1997 03:42:00 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Takasaki",
"Kanehisa",
""
]
] |
solv-int/9705017 | Eugene Ferapontov | E.V. Ferapontov (Institute for Mathematical Modelling, Moscow) | Laplace transformations of hydrodynamic type systems in Riemann
invariants: periodic sequences | 22 pages, Latex | null | 10.1088/0305-4470/30/19/023 | null | solv-int nlin.SI | null | The conserved densities of hydrodynamic type system in Riemann invariants
satisfy a system of linear second order partial differential equations. For
linear systems of this type Darboux introduced Laplace transformations,
generalising the classical transformations in the scalar case. It is
demonstrated that Laplace transformations can be pulled back to the
transformations of the corresponding hydrodynamic type systems. We discuss
periodic Laplace sequences of with the emphasize on the simplest nontrivial
case of period 2. For 3-component systems in Riemann invariants a complete
discription of closed quadruples is proposed. They turn to be related to a
special quadratic reduction of the (2+1)-dimensional 3-wave system which can be
reduced to a triple of pairwize commuting Monge-Ampere equations. In terms of
the Lame and rotation coefficients Laplace transformations have a natural
interpretation as the symmetries of the Dirac operator, associated with the
(2+1)-dimensional n-wave system. The 2-component Laplace transformations can be
interpreted also as the symmetries of the (2+1)-dimensional integrable
equations of Davey-Stewartson type. Laplace transformations of hydrodynamic
type systems originate from a canonical geometric correspondence between
systems of conservation laws and line congruences in projective space.
| [
{
"version": "v1",
"created": "Wed, 28 May 1997 15:40:33 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Ferapontov",
"E. V.",
"",
"Institute for Mathematical Modelling, Moscow"
]
] |
solv-int/9705018 | Fritz Gesztesy | Fritz Gesztesy and Rudi Weikard | A Characterization of All Elliptic Solutions of the AKNS Hierarchy | LaTeX | null | null | null | solv-int nlin.SI | null | An explicit characterization of all elliptic algebro-geometric solutions of
the AKNS hierarchy is presented. Our approach is based on (an extension of) a
classical theorem of Picard, which guarantees the existence of solutions which
are elliptic of the second kind for n-th order ordinary differential equations
with elliptic coefficients associated with a common period lattice. As
by-products we offer a detailed Floquet analysis of Dirac-type differential
expressions with periodic coefficients, specifically emphasizing
algebro-geometric coefficients, and a constructive reduction of singular
hyperelliptic curves and their Baker-Akhiezer functions to the nonsingular
case.
| [
{
"version": "v1",
"created": "Wed, 28 May 1997 22:55:45 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Gesztesy",
"Fritz",
""
],
[
"Weikard",
"Rudi",
""
]
] |
solv-int/9705019 | Fritz Gesztesy | W. Bulla, F. Gesztesy, H. Holden, and G. Teschl | Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and
Kac-van Moerbeke Hierarchies | LaTeX, to appear in Memoirs of the Amer. Math. Soc | Memoirs of the Amer. Math. Soc. 135/641, 1998 | 10.1090/memo/0641 | null | solv-int math.SP nlin.SI | null | Combining algebro-geometric methods and factorization techniques for finite
difference expressions we provide a complete and self-contained treatment of
all real-valued quasi-periodic finite-gap solutions of both the Toda and
Kac-van Moerbeke hierarchies. In order to obtain our principal new result, the
algebro-geometric finite-gap solutions of the Kac-van Moerbeke hierarchy, we
employ particular commutation methods in connection with Miura-type
transformations which enable us to transfer whole classes of solutions (such as
finite-gap solutions) from the Toda hierarchy to its modified counterpart, the
Kac-van Moerbeke hierarchy, and vice versa.
| [
{
"version": "v1",
"created": "Thu, 29 May 1997 22:29:12 GMT"
}
] | 2015-09-29T00:00:00 | [
[
"Bulla",
"W.",
""
],
[
"Gesztesy",
"F.",
""
],
[
"Holden",
"H.",
""
],
[
"Teschl",
"G.",
""
]
] |
solv-int/9706001 | Harry Braden | H. W. Braden | R-Matrices and Generalized Inverses | 11 pages, Latex | null | null | MS-97-006 | solv-int nlin.SI | null | Four results are given that address the existence, ambiguities and
construction of a classical R-matrix given a Lax pair. They enable the uniform
construction of R-matrices in terms of any generalized inverse of $ad L$. For
generic $L$ a generalized inverse (and indeed the Moore-Penrose inverse) is
explicitly constructed. The R-matrices are in general momentum dependent and
dynamical. The construction applies equally to Lax matrices with spectral
parameter.
| [
{
"version": "v1",
"created": "Fri, 30 May 1997 14:29:46 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Braden",
"H. W.",
""
]
] |
solv-int/9706002 | John Harnad | J. Harnad and Alexander R. Its | Integrable Fredholm Operators and Dual Isomonodromic Deformations | PlainTeX 32gs | Commun.Math.Phys.226:497-530,2002 | 10.1007/s002200200614 | CRM 2477 (1997) | solv-int cond-mat hep-th math-ph math.MP nlin.SI | null | The Fredholm determinants of a special class of integral operators K
supported on the union of m curve segments in the complex plane are shown to be
the tau-functions of an isomonodromic family of meromorphic covariant
derivative operators D_l. These have regular singular points at the 2m
endpoints of the curve segments and a singular point of Poincare index 1 at
infinity. The rank r of the vector bundle over the Riemann sphere on which they
act equals the number of distinct terms in the exponential sums entering in the
numerator of the integral kernels. The deformation equations may be viewed as
nonautonomous Hamiltonian systems on an auxiliary symplectic vector space M,
whose Poisson quotient, under a parametric family of Hamiltonian group actions,
is identified with a Poisson submanifold of the loop algebra Lgl_R(r) with
respect to the rational R-matrix structure. The matrix Riemann-Hilbert problem
method is used to identify the auxiliary space M with the data defining the
integral kernel of the resolvent operator at the endpoints of the curve
segments. A second associated isomonodromic family of covariant derivative
operators D_z is derived, having rank n=2m, and r finite regular singular
points at the values of the exponents defining the kernel of K. This family is
similarly embedded into the algebra Lgl_R(n) through a dual parametric family
of Poisson quotients of M. The operators D_z are shown to be analogously
associated to the integral operator obtained from K through a Fourier-Laplace
transform.
| [
{
"version": "v1",
"created": "Thu, 5 Jun 1997 02:02:19 GMT"
}
] | 2009-01-23T00:00:00 | [
[
"Harnad",
"J.",
""
],
[
"Its",
"Alexander R.",
""
]
] |
solv-int/9706003 | Mts | R. A. Sharipov (Bashkir State University, Ufa, Russia) | On the point transformations for the equation $y''= P + 3Qy' + 3R{y'}^2
+ S{y'}^3$ | AmS-TeX, Version 2.1, amsppt style, 36 pages | null | null | null | solv-int nlin.SI | null | For the equations $y''=P(x,y) + 3Q(x,y)y' + 3R(x,y){y'}^2 + S(x,y){y'}^3$ the
problem of equivalence is considered. Some classical results are resumed in
order to prepare the background for the study of special subclass of such
equations, which arises in the theory of dynamical systems admitting the normal
shift.
| [
{
"version": "v1",
"created": "Thu, 5 Jun 1997 05:56:27 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Sharipov",
"R. A.",
"",
"Bashkir State University, Ufa, Russia"
]
] |
solv-int/9706004 | J. vandeLeur | G.F. Helminck, J.W. van de Leur | An analytic description of the vector constrained KP hierarchy | 15 pages, Latex2e | null | 10.1007/s002200050341 | null | solv-int hep-th math.QA nlin.SI q-alg | null | In this paper we give a geometric description in terms of the Grassmann
manifold of Segal and Wilson, of the reduction of the KP hierarchy known as the
vector $k$-constrained KP hierarchy. We also show in a geometric way that these
hierarchies are equivalent to Krichever's general rational reductions of the KP
hierarchy.
| [
{
"version": "v1",
"created": "Thu, 5 Jun 1997 11:25:36 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Helminck",
"G. F.",
""
],
[
"van de Leur",
"J. W.",
""
]
] |
solv-int/9706005 | Jose Carlos Brunelli | J. C. Brunelli and A. Das | A Lax Description for Polytropic Gas Dynamics | 9 pages, TeX | Phys.Lett. A235 (1997) 597-602 | 10.1016/S0375-9601(97)00708-1 | null | solv-int hep-th nlin.SI | null | We give a Lax description for the system of polytropic gas equations. The
special structure of the Lax function naturally leads to the two infinite sets
of conserved charges associated with this system. We obtain closed form
expressions for the conserved charges as well as the generating functions for
them. We show how the study of these generating functions can naturally lead to
the recursion relation between the conserved quantities as well as the higher
order Hamiltonian structures.
| [
{
"version": "v1",
"created": "Thu, 5 Jun 1997 13:34:30 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Brunelli",
"J. C.",
""
],
[
"Das",
"A.",
""
]
] |
solv-int/9706006 | J. vandeLeur | Victor Kac, Johan van de Leur | The geometry of spinors and the multicomponent BKP and DKP hierarchies | 46 pages, Latex2e | null | null | null | solv-int hep-th math.QA nlin.SI q-alg | null | We develop a formalism of multicomponent BKP hierarchies using elementary
geometry of spinors. The multicomponent KP and the modified KP hierarchy (hence
all their reductions like KdV, NLS, AKNS or DS) are reductions of the
multicomponent BKP.
| [
{
"version": "v1",
"created": "Fri, 6 Jun 1997 10:26:41 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Kac",
"Victor",
""
],
[
"van de Leur",
"Johan",
""
]
] |
solv-int/9706007 | Robert Milson | Robert Milson | On the Liouville transformation and exactly-solvable Schrodinger
equations | 16 pages, 6 figures | null | null | null | solv-int nlin.SI | null | The present article discusses the connection between exactly-solvable
Schrodinger equations and the Liouville transformation. This transformation
yields a large class of exactly-solvable potentials, including the
exactly-solvable potentials introduced by Natanzon. As well, this class is
shown to contain two new families of exactly solvable potentials.
| [
{
"version": "v1",
"created": "Sun, 15 Jun 1997 22:33:59 GMT"
},
{
"version": "v2",
"created": "Tue, 21 Oct 1997 18:14:09 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Milson",
"Robert",
""
]
] |
solv-int/9706008 | Yuly Billig | Yuly Billig | An Extension of the KdV Hierarchy Arising from a Representation of a
Toroidal Lie Algebra | 22 pages, plain tex, no figures | null | null | null | solv-int nlin.SI | null | In this article we show how to construct hierarchies of partial differential
equations from the vertex operator representations of toroidal Lie algebras. In
the smallest example - rank 2 toroidal cover of $sl_2$ - we obtain an extension
of the KdV hierarchy. We use the action of the corresponding
infinite-dimensional group to construct solutions for these non-linear PDEs.
| [
{
"version": "v1",
"created": "Wed, 18 Jun 1997 19:43:58 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Billig",
"Yuly",
""
]
] |
Subsets and Splits