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sequence |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
solv-int/9712016 | Pierre Vandergheynst | M. Adler and P. van Moerbeke | Toda-Darboux maps and vertex operators | 23 pages, LaTeX | null | null | Math-97 | solv-int nlin.SI | null | The purpose of this paper is to study Toda-Darboux transforms, i.e., Darboux
transforms for operators L(t) flowing according to the Toda lattice. Each
element of the null-space $L(t)-z$ specifies a factorization for all t and thus
a Toda-Darboux transform on $L(t)$. The Toda-Darboux map induces a
transformation on the tau-vectors, given by a certain vertex operator, and on
eigenfunctions, given by a Wronskian. .
| [
{
"version": "v1",
"created": "Fri, 19 Dec 1997 15:07:32 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Adler",
"M.",
""
],
[
"van Moerbeke",
"P.",
""
]
] |
solv-int/9712017 | Adam Doliwa | A. Doliwa, P. M. Santini and M. Manas | Transformations of Quadrilateral Lattices | 50 pages, 15 figures; minor corrections, added references | J. Math. Phys. 41 (2000) 944-990 | 10.1063/1.533175 | null | solv-int nlin.SI | null | Motivated by the classical studies on transformations of conjugate nets, we
develop the general geometric theory of transformations of their discrete
analogues: the multidimensional quadrilateral lattices, i.e. lattices x: Z^N ->
R^M, whose elementary quadrilaterals are planar. Our investigation is based on
the discrete analogue of the theory of the rectilinear congruences, which we
also present in detail. We study, in particular, the discrete analogues of the
Laplace, Combescure, Levy, radial and fundamental transformations and their
interrelations. The composition of these transformations and their
permutability is also investigated from a geometric point of view. The deep
connections between "transformations" and "discretizations" is also
investigated for quadrilateral lattices. We finally interpret these results
within the D-bar formalism.
| [
{
"version": "v1",
"created": "Sat, 20 Dec 1997 11:02:51 GMT"
},
{
"version": "v2",
"created": "Sat, 17 Jan 1998 13:00:30 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Doliwa",
"A.",
""
],
[
"Santini",
"P. M.",
""
],
[
"Manas",
"M.",
""
]
] |
solv-int/9712018 | Metin Gurses | Metin Gurses | Sigma Models and Minimal Surfaces | Latex, 13pp, to be published in Letters in Mathematical Physics | null | null | null | solv-int nlin.SI | null | The correspondance is established between the sigma models, the minimal
surfaces and the Monge-Ampere equation. The Lax -Pairs of the minimality
condition of the minimal surfaces and the Monge-Ampere equations are given.
Existance of infinitely many nonlocal conservation laws is shown and some
Backlund transformations are also given.
| [
{
"version": "v1",
"created": "Tue, 23 Dec 1997 12:29:14 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Gurses",
"Metin",
""
]
] |
solv-int/9712019 | Matveev V. S. | V.S. Matveev (Bremen University) | Quadratically integrable geodesic flows on the torus and on the Klein
bottle | 10 pages, latex2e | Regular and Chaotic Dynamics, vol 2 no 1 (1997), 96-103 | null | null | solv-int math.DG nlin.SI | null | In the present paper we prove, that if the geodesic flow of a metric G on the
torus T is quadratically integrable, then the torus T isometrically covers a
torus with a Liouville metric on it, and describe the set of quadratically
integrable geodesic flows on the Klein bottle.
| [
{
"version": "v1",
"created": "Tue, 23 Dec 1997 16:41:50 GMT"
}
] | 2011-08-22T00:00:00 | [
[
"Matveev",
"V. S.",
"",
"Bremen University"
]
] |
solv-int/9712020 | Valery Shchesnovich | V.S. Shchesnovich | Polarization scattering by soliton-soliton collisions | Second formula in Eq. (7) is corrected; 5 pages, Latex | null | null | null | solv-int nlin.SI | null | Collision of two solitons of the Manakov system is analytically studied.
Existence of a complete polarization mode switching regime is proved and the
parameters of solitons prepared for polarization switching are found.
| [
{
"version": "v1",
"created": "Wed, 24 Dec 1997 19:03:51 GMT"
},
{
"version": "v2",
"created": "Wed, 14 Jan 1998 10:06:15 GMT"
},
{
"version": "v3",
"created": "Fri, 30 Jan 1998 12:28:28 GMT"
},
{
"version": "v4",
"created": "Tue, 9 Dec 2003 19:00:52 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Shchesnovich",
"V. S.",
""
]
] |
solv-int/9801001 | Arthur Vartanian | A. V. Kitaev, A. H. Vartanian | Asymptotics of Solutions to the Modified Nonlinear Schr\"{o}dinger
Equation: Solitons on a Non-Vanishing Continuous Background | 38 pages, 1 figure, LaTeX | null | null | null | solv-int nlin.SI | null | Using the matrix Riemann-Hilbert factorization approach for nonlinear
evolution systems which take the form of Lax-pair isospectral deformations and
whose corresponding Lax operators contain both discrete and continuous spectra,
the leading-order asymptotics as $t \to \pm \infty$ of the solution to the
Cauchy problem for the modified nonlinear Schr\"{o}dinger equation, $i
\partial_{t} u + {1/2} \partial_{x}^{2} u + | u |^{2} u + i s \partial_{x} (| u
|^{2} u) = 0$, $s \in \Bbb R_{>0}$, which is a model for nonlinear pulse
propagation in optical fibers in the subpicosecond time scale, are obtained:
also derived are analogous results for two gauge-equivalent nonlinear evolution
equations; in particular, the derivative nonlinear Schr\"{o}dinger equation, $i
\partial_{t} q + \partial_{x}^{2} q - i \partial_{x} (| q |^{2} q) = 0$. As an
application of these asymptotic results, explicit expressions for position and
phase shifts of solitons in the presence of the continuous spectrum are
calculated.
| [
{
"version": "v1",
"created": "Sat, 27 Dec 1997 14:16:23 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Kitaev",
"A. V.",
""
],
[
"Vartanian",
"A. H.",
""
]
] |
solv-int/9801002 | Nobuhiko Shinzawa | Nobuhiko Shinzawa and Satoru Saito | A Symmetric Generalization of Linear B\"acklund Transformation
associated with the Hirota Bilinear Difference Equation | Latex, 12 pages, 1 figure | null | 10.1088/0305-4470/31/19/016 | null | solv-int nlin.SI | null | The Hirota bilinear difference equation is generalized to discrete space of
arbitrary dimension. Solutions to the nonlinear difference equations can be
obtained via B\"acklund transformation of the corresponding linear problems.
| [
{
"version": "v1",
"created": "Wed, 31 Dec 1997 02:31:58 GMT"
}
] | 2015-06-26T00:00:00 | [
[
"Shinzawa",
"Nobuhiko",
""
],
[
"Saito",
"Satoru",
""
]
] |
solv-int/9801003 | YU-Song Ju | Yu. S.J(1), K. Toda(1),N. Sasa(2) and T. Fukuyama(1)((1)Ritsumeikan
Univ., (2)Japan Atomic Energy Research Institute) | N Soliton Solutions to The Bogoyavlenskii-Schiff Equation and A Quest
for The Soliton Solution in (3 + 1) Dimensions | 14 pages, 8 figures([email protected]), uses ioplppt.sty | null | null | null | solv-int nlin.SI | null | We study the integrable systems in higher dimensions which can be written not
by the Hirota's bilinear form but by the trilinear form. We explicitly discuss
about the Bogoyavlenskii-Schiff(BS) equation in (2 + 1) dimensions. Its
analytical proof of multi soliton solution and a new feature are given. Being
guided by the strong symmetry, we also propose a new equation in (3 + 1)
dimensions.
| [
{
"version": "v1",
"created": "Sat, 3 Jan 1998 02:51:43 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"J",
"Yu. S.",
""
],
[
"Toda",
"K.",
""
],
[
"Sasa",
"N.",
""
],
[
"Fukuyama",
"T.",
""
]
] |
solv-int/9801004 | Andrei Pronko | A. G. Izergin, A. G. Pronko | Temperature correlators in the two-component one-dimensional gas | 40 pages, LaTeX, a4.sty | null | 10.1016/S0550-3213(98)00182-5 | PDMI PREPRINT - 19/1997 | solv-int nlin.SI | null | The quantum nonrelativistic two-component Bose and Fermi gases with the
infinitely strong point-like coupling between particles in one space dimension
are considered. Time and temperature dependent correlation functions are
represented in the thermodynamic limit as Fredholm determinants of integrable
linear integral operators.
| [
{
"version": "v1",
"created": "Sat, 3 Jan 1998 16:07:25 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Izergin",
"A. G.",
""
],
[
"Pronko",
"A. G.",
""
]
] |
solv-int/9801005 | null | Shigeki Matsutani | Statistical Mechanics of Non-stretching Elastica in Three Dimensional
Space | AMS-Tex Use | null | 10.1016/S0393-0440(98)00042-4 | null | solv-int nlin.SI | null | Recently I proposed a new calculation scheme of a partition function of an
immersion object using path integral method and theory of soliton (to appear in
J.Phys.A). I applied the scheme to problem of elastica in two-dimensional space
and Willmore surface in three dimensional space. In this article, I will apply
the scheme to elastica in three dimensional space as a more physical model in
polymer science. Then orbit space of the nonlinear Schrodinger and complex
modified Korteweg-de Vries equations can be regarded as the functional space of
the partition function. By investigation of the partition function, I gives a
conjecture of the relation of these soliton equations.
| [
{
"version": "v1",
"created": "Sun, 4 Jan 1998 07:13:18 GMT"
},
{
"version": "v2",
"created": "Sat, 7 Mar 1998 03:05:12 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Matsutani",
"Shigeki",
""
]
] |
solv-int/9801006 | null | Shigeki Matsutani | Dirac Operator of a Conformal Surface Immersed in R^4: Further
Generalized Weierstrass Relation | AMS-Tex Use | null | null | null | solv-int nlin.SI | null | In the previous report (J. Phys. A (1997) 30 4019-4029), I showed that the
Dirac operator defined over a conformal surface immersed in R^3 is identified
with the Dirac operator which is generalized the Weierstrass- Enneper equation
and Lax operator of the modified Novikov-Veselov (MNV) equation. In this
article, I determine the Dirac operator defined over a conformal surface
immersed in R^4, which is reduced to the Lax operators of the nonlinear
Schrodinger and the MNV equations by taking appropriate limits. Thus the Dirac
operator might be the Lax operator of (2+1)- dimensional soliton equation.
| [
{
"version": "v1",
"created": "Sun, 4 Jan 1998 07:20:41 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Matsutani",
"Shigeki",
""
]
] |
solv-int/9801007 | Hasan Gumral | Hasan Gumral | General vorticity conservation | Latex, 20 pages | null | null | null | solv-int nlin.SI | null | The motion of an incompressible fluid in Lagrangian coordinates involves
infinitely many symmetries generated by the left Lie algebra of group of volume
preserving diffeomorphisms of the three dimensional domain occupied by the
fluid. Utilizing a 1+3-dimensional Hamiltonian setting an explicit realization
of this symmetry algebra and the related Lagrangian and Eulerian conservation
laws are constructed recursively. Their Lie algebraic structures are inherited
from the same construction. The laws of general vorticity and helicity
conservations are formulated globally in terms of invariant differential forms
of the velocity field.
| [
{
"version": "v1",
"created": "Mon, 5 Jan 1998 20:52:37 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Gumral",
"Hasan",
""
]
] |
solv-int/9801008 | Harold Widom | Craig A. Tracy, Harold Widom | Asymptotics of a class of Fredholm determinants | 8 pages, LaTeX file | "Spectral Problems in Geometry and Arithmetic," ed. T. Branson,
Amer. Math. Soc., Providence, 1999, pgs 167-174 | null | null | solv-int math.FA nlin.SI | null | In this expository article we describe the asymptotics of certain Fredholm
determinants which provide solutions to the cylindrical Toda equations, and we
explain how these asymptotics are derived. The connection with Fredholm
determinants arising in the theory of random matrices, and their asymptotics,
are also discussed.
| [
{
"version": "v1",
"created": "Mon, 5 Jan 1998 21:21:59 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Tracy",
"Craig A.",
""
],
[
"Widom",
"Harold",
""
]
] |
solv-int/9801009 | Szmigielski | J. Dorfmeister, H. Gradl and J. Szmigielski | Systems of PDEs obtained from factorization in loop groups | 1 figure | null | null | null | solv-int nlin.SI | null | We propose a generalization of a Drinfeld-Sokolov scheme of attaching
integrable systems of PDEs to affine Kac-Moody algebras. With every affine
Kac-Moody algebra $\gg$ and a parabolic subalgebra $\gp$, we associate two
hierarchies of PDEs. One, called positive, is a generalization of the KdV
hierarchy, the other, called negative, generalizes the Toda hierarchy. We prove
a coordinatization theorem, which establishes that the number of functions
needed to express all PDEs of the the total hierarchy equals the rank of $\gg$.
The choice of functions, however, is shown to depend in a noncanonical way on
$\gp$. We employ a version of the Birkhoff decomposition and a ``2-loop''
formulation which allows us to incorporate geometrically meaningful solutions
to those hierarchies. We illustrate our formalism for positive hierarchies with
a generalization of the Boussinesq system and for the negative hierarchies with
the stationary Bogoyavlenskii equation.
| [
{
"version": "v1",
"created": "Thu, 8 Jan 1998 17:34:51 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Dorfmeister",
"J.",
""
],
[
"Gradl",
"H.",
""
],
[
"Szmigielski",
"J.",
""
]
] |
solv-int/9801010 | David H. Sattinger | Richard Beals and D. H. Sattinger | Integrable Systems and Isomonodromy Deformations | null | Physica D, vol 65, (1993), 17-47 | 10.1016/0167-2789(93)90003-J | null | solv-int nlin.SI | null | We analyze in detail three classes of isomondromy deformation problems
associated with integrable systems. The first two are related to the scaling
invariance of the $n\times n$ AKNS hierarchies and the Gel'fand-Dikii
hierarchies. The third arises in string theory as the representation of the
Heisenberg group by $[(L^{k/n})_+,L]=I$ where $L$ is an $n^{th}$ order scalar
differential operator. The monodromy data is constructed in each case; the
inverse monodromy problem is solved as a Riemann-Hilbert problem; and a simple
proof of the Painlev\'e property is given for the general case
| [
{
"version": "v1",
"created": "Thu, 8 Jan 1998 22:51:09 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Beals",
"Richard",
""
],
[
"Sattinger",
"D. H.",
""
]
] |
solv-int/9801011 | David H. Sattinger | D.H. Sattinger and J.S. Szmigielski | Factorization and the Dressing Method for the Gel'fand-Dikii Hierarch | null | Physica D, vol 64, (1993), 1-34 | 10.1016/0167-2789(93)90247-X | null | solv-int nlin.SI | null | The isospectral flows of an $n^{th}$ order linear scalar differential
operator $L$ under the hypothesis that it possess a Baker-Akhiezer function
were originally investigated by Segal and Wilson from the point of view of
infinite dimensional Grassmanians, and the reduction of the KP hierarchy to the
Gel'fand-Dikii hierarchy. The associated first order systems and their formal
asymptotic solutions have a rich Lie algebraic structure which was investigated
by Drinfeld and Sokolov. We investigate the matrix Riemann-Hilbert
factorizations for these systems, and show that different factorizations lead
respectively to the potential, modified, and ordinary Gel'fand-Dikii flows. Lie
algebra decompositions (the Adler-Kostant-Symes method) are obtained for the
modified and potential flows. For $n>3$ the appropriate factorization for the
Gel'fand-Dikii flows is not a group factorization, as would be expected; yet a
modification of the dressing method still works.
A direct proof, based on a Fredholm determinant associated with the
factorization problem, is given that the potentials are meromorphic in $x$ and
in the time variables. Potentials with Baker-Akhiezer functions include the
multisoliton and rational solutions, as well as potentials in the scattering
class with compactly supported scattering data. The latter are dense in the
scattering class.
| [
{
"version": "v1",
"created": "Thu, 8 Jan 1998 23:19:41 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Sattinger",
"D. H.",
""
],
[
"Szmigielski",
"J. S.",
""
]
] |
solv-int/9801012 | Andrey V. Tsiganov | Andrey Tsiganov | Dynamical boundary conditions for integrable lattices | LaTeX, 12pages | J. Phys. A, Math. Gen. 31, No.39, 8049-8061, (1998) | 10.1088/0305-4470/31/39/017 | null | solv-int nlin.SI | null | Some special solutions to the reflection equation are considered. These
boundary matrices are defined on the common quantum space with the other
operators in the chain. The relations with the Drinfeld twist are discussed.
| [
{
"version": "v1",
"created": "Fri, 9 Jan 1998 07:26:50 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Tsiganov",
"Andrey",
""
]
] |
solv-int/9801013 | Igor G. Korepanov | Igor G. Korepanov | Particles and strings in a (2+1)-D integrable quantum model | null | J. Nonlinear Math. Phys. 7 (2000), no. 1, 94-119 | 10.2991/jnmp.2000.7.1.7 | JNMP 4/2002 (Review Article) | solv-int nlin.SI | null | We give a review of some recent work on generalization of the Bethe ansatz in
the case of $2+1$-dimensional models of quantum field theory. As such a model,
we consider one associated with the tetrahedron equation, i.e. the
$2+1$-dimensional generalization of the famous Yang--Baxter equation. We
construct some eigenstates of the transfer matrix of that model. There arise,
together with states composed of point-like particles analogous to those in the
usual $1+1$-dimensional Bethe ansatz, new string-like states and
string-particle hybrids.
| [
{
"version": "v1",
"created": "Fri, 9 Jan 1998 09:17:41 GMT"
},
{
"version": "v2",
"created": "Wed, 29 Mar 2000 13:14:11 GMT"
},
{
"version": "v3",
"created": "Sat, 1 Jan 2000 00:00:00 GMT"
}
] | 2015-06-26T00:00:00 | [
[
"Korepanov",
"Igor G.",
""
]
] |
solv-int/9801014 | Oleg M. Kiselev | R.R. Gadyl'shin, O.M. Kiselev (Institute of Mathematics, Ufa Science
Centre, Russian Acad. of Sciences) | Asymptotics of perturbed soliton for Davey--Stewartson II equation | In this replaced version the formula for the perturbed parameter of
the soliton is corrected. Amstex, 13 pages | null | null | null | solv-int nlin.SI | null | It is shown that, under a small perturbation of lump (soliton) for
Davey--Stewartson (DS-II) equation, the scattering data gain the nonsoliton
structure. As a result, the solution has the form of Fourier type integral.
Asymptotic analysis shows that, in spite of dispertion, the principal term of
the asymptotic expansion for the solution has the solitary wave form up to
large time.
| [
{
"version": "v1",
"created": "Fri, 9 Jan 1998 14:50:06 GMT"
},
{
"version": "v2",
"created": "Tue, 31 Mar 1998 16:54:35 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Gadyl'shin",
"R. R.",
"",
"Institute of Mathematics, Ufa Science\n Centre, Russian Acad. of Sciences"
],
[
"Kiselev",
"O. M.",
"",
"Institute of Mathematics, Ufa Science\n Centre, Russian Acad. of Sciences"
]
] |
solv-int/9801015 | Igor G. Korepanov | R.M. Kashaev, I.G. Korepanov, S.M. Sergeev | Functional Tetrahedron Equation | LaTeX, 16 pages | Theor. Math. Phys. 117:3 (1998) 1402 - 1413; Teor. Mat. Fiz. 117:3
(1998) 370 - 384 | 10.1007/BF02557179 | null | solv-int nlin.SI | null | We describe a scheme of constructing classical integrable models in
2+1-dimensional discrete space-time, based on the functional tetrahedron
equation - equation that makes manifest the symmetries of a model in local
form. We construct a very general "block-matrix model" together with its
algebro-geometric solutions, study its various particular cases, and also
present a remarkably simple scheme of quantization for one of those cases.
| [
{
"version": "v1",
"created": "Tue, 13 Jan 1998 11:53:59 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Kashaev",
"R. M.",
""
],
[
"Korepanov",
"I. G.",
""
],
[
"Sergeev",
"S. M.",
""
]
] |
solv-int/9801016 | Evgeny Doktorov | V.S. Shchesnovich and E.V. Doktorov | Perturbation theory for the modified nonlinear Schr{\"o}dinger solitons | 22 pages, Latex, no figures. Submitted to Physica D | null | 10.1016/S0167-2789(98)00209-7 | null | solv-int nlin.PS nlin.SI patt-sol | null | The perturbation theory based on the Riemann-Hilbert problem is developed for
the modified nonlinear Schr{\"o}dinger equation which describes the propagation
of femtosecond optical pulses in nonlinear single-mode optical fibers. A
detailed analysis of the adiabatic approximation to perturbation-induced
evolution of the soliton parameters is given. The linear perturbation and the
Raman gain are considered as examples.
| [
{
"version": "v1",
"created": "Wed, 14 Jan 1998 09:35:00 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Shchesnovich",
"V. S.",
""
],
[
"Doktorov",
"E. V.",
""
]
] |
solv-int/9801017 | Kjell Rosquist | Kjell Rosquist | The classical r-matrix in a geometric framework | LaTeX2e file; requires amsmath,eufrak and eucal packages | null | 10.1016/S0375-9601(99)00177-2 | USITP 98-01 | solv-int math-ph math.MP nlin.SI | null | We use a Riemannian (or pseudo-Riemannian) geometric framework to formulate
the theory of the classical r-matrix for integrable systems. In this picture
the r-matrix is related to a fourth rank tensor, named the r-tensor, on the
configuration space. The r-matrix itself carries one connection type index and
three tensorial indices. Being defined on the configuration space it has no
momentum dependence but is dynamical in the sense of depending on the
configuration variables. The tensorial nature of the r-matrix is used to derive
its transformation properties. The resulting transformation formula turns out
to be valid for a general r-matrix structure independently of the geometric
framework. Moreover, the entire structure of the r-matrix equation follows
directly from a simple covariant expression involving the Lax matrix and its
covariant derivative. Therefore it is argued that the geometric formulation
proposed here helps to improve the understanding of general r-matrix
structures. It is also shown how the Jacobi identity gives rise to a
generalized dynamical classical Yang-Baxter equation involving the Riemannian
curvature.
| [
{
"version": "v1",
"created": "Thu, 15 Jan 1998 10:26:42 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Rosquist",
"Kjell",
""
]
] |
solv-int/9801018 | Krzysztof Kowalski | Krzysztof Kowalski | Nonlinear dynamical systems and classical orthogonal polynomials | 21 pages latex, uses revtex | J. Math. Phys. 38 (1997) 2483-2505 | 10.1063/1.531990 | kft-97-45 | solv-int nlin.SI quant-ph | null | It is demonstrated that nonlinear dynamical systems with analytic
nonlinearities can be brought down to the abstract Schr\"odinger equation in
Hilbert space with boson Hamiltonian. The Fourier coefficients of the expansion
of solutions to the Schr\"odinger equation in the particular occupation number
representation are expressed by means of the classical orthogonal polynomials.
The introduced formalism amounts a generalization of the classical methods for
linearization of nonlinear differential equations such as the Carleman
embedding technique and Koopman approach.
| [
{
"version": "v1",
"created": "Wed, 14 Jan 1998 15:47:51 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Kowalski",
"Krzysztof",
""
]
] |
solv-int/9801019 | Ming-Hsien Tu | Wen-Jui Huang, Jiin-Chang Shaw and Ming-Hsien Tu | Matrix Formulation of Hamiltonian Structures of Constrained KP Hierarchy | 19 pages, Revtex, no figures. Minor changes, reference corrected | J. Math. Phys. 39 (1998) 3738 | 10.1063/1.532464 | null | solv-int nlin.SI | null | We give a matrix formulation of the Hamiltonian structures of constrained KP
hierarchy. First, we derive from the matrix formulation the Hamiltonian
structure of the one-constraint KP hierarchy, which was originally obtained by
Oevel and Strampp. We then generalize the derivation to the multi-constraint
case and show that the resulting bracket is actually the second Gelfand-Dickey
bracket associated with the corresponding Lax operator. The matrix formulation
of the Hamiltonian structure of the one-constraint KP hierarchy in the form
introduced in the study of matrix model is also discussed
| [
{
"version": "v1",
"created": "Thu, 15 Jan 1998 03:43:29 GMT"
},
{
"version": "v2",
"created": "Thu, 22 Jan 1998 06:07:12 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Huang",
"Wen-Jui",
""
],
[
"Shaw",
"Jiin-Chang",
""
],
[
"Tu",
"Ming-Hsien",
""
]
] |
solv-int/9801020 | Krzysztof Kowalski | Krzysztof Kowalski | Universal formats for nonlinear dynamical systems | 9 pages LaTeX | Chem. Phys. Lett. 209 (1993) 167 -170 | null | DB-93-17 | solv-int chao-dyn nlin.CD nlin.SI | null | It is demonstrated that very general nonlinear dynamical systems covering all
cases arising in practice can be brought down to rate equations of chemical
kinetics
| [
{
"version": "v1",
"created": "Thu, 15 Jan 1998 08:17:58 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Kowalski",
"Krzysztof",
""
]
] |
solv-int/9801021 | Henrik Aratyn | H. Aratyn, E. Nissimov and S. Pacheva | Supersymmetric KP Hierarchy: ``Ghost'' Symmetry Structure, Reductions
and Darboux-Backlund Solutions | Minor corrections in few equations. LaTeX, 12 pgs | null | 10.1063/1.532736 | BGU-98/01/Jan-PH, UICHEP-TH/98-1 | solv-int hep-th nlin.SI | null | This paper studies Manin-Radul supersymmetric KP hierarchy (MR-SKP) in three
related aspects: (i) We find an infinite set of additional (``ghost'') symmetry
flows spanning the same (anti-)commutation algebra as the ordinary MR-SKP
flows; (ii) The latter are used to construct consistent reductions of the
initial unconstrained MR-SKP hierarchy which involves a nontrivial modification
for the fermionic flows; (iii) For the simplest constrained MR-SKP hierarchy we
show that the orbit of Darboux-Backlund transformations lies on a
supersymmetric Toda lattice being a square-root of the standard one-dimensional
Toda lattice, and also we find explicit Wronskian-ratio solutions for the
super-tau function.
| [
{
"version": "v1",
"created": "Thu, 15 Jan 1998 18:33:08 GMT"
},
{
"version": "v2",
"created": "Thu, 5 Feb 1998 00:41:28 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Aratyn",
"H.",
""
],
[
"Nissimov",
"E.",
""
],
[
"Pacheva",
"S.",
""
]
] |
solv-int/9801022 | Anton Zabrodin | I.Krichever and A.Zabrodin | Vacuum curves of elliptic L-operators and representations of Sklyanin
algebra | 27 pages, latex, typos corrected | null | null | ITEP-TH-76/97 | solv-int hep-th nlin.SI | null | An algebro-geometric approach to representations of Sklyanin algebra is
proposed. To each 2 \times 2 quantum L-operator an algebraic curve
parametrizing its possible vacuum states is associated. This curve is called
the vacuum curve of the L-operator. An explicit description of the vacuum curve
for quantum L-operators of the integrable spin chain of XYZ type with arbitrary
spin $\ell$ is given. The curve is highly reducible. For half-integer $\ell$ it
splits into $\ell +{1/2}$ components isomorphic to an elliptic curve. For
integer $\ell$ it splits into $\ell$ elliptic components and one rational
component. The action of elements of the L-operator to functions on the vacuum
curve leads to a new realization of the Sklyanin algebra by difference
operators in two variables restricted to an invariant functional subspace.
| [
{
"version": "v1",
"created": "Thu, 22 Jan 1998 20:03:38 GMT"
},
{
"version": "v2",
"created": "Wed, 20 May 1998 15:18:44 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Krichever",
"I.",
""
],
[
"Zabrodin",
"A.",
""
]
] |
solv-int/9801023 | null | Unal Goktas (1), Willy Hereman (1) ((1) Colorado School of Mines) | Computation of conservation laws for nonlinear lattices | To appear in Physica D, 17 pages, Latex, uses the style files
elsart.sty and elsart12.sty | null | 10.1016/S0167-2789(98)00140-7 | null | solv-int nlin.SI | null | An algorithm to compute polynomial conserved densities of polynomial
nonlinear lattices is presented. The algorithm is implemented in Mathematica
and can be used as an automated integrability test. With the code diffdens.m,
conserved densities are obtained for several well-known lattice equations. For
systems with parameters, the code allows one to determine the conditions on
these parameters so that a sequence of conservation laws exist.
| [
{
"version": "v1",
"created": "Thu, 22 Jan 1998 20:59:48 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Goktas",
"Unal",
"",
"Colorado School of Mines"
],
[
"Hereman",
"Willy",
"",
"Colorado School of Mines"
]
] |
solv-int/9801024 | null | Unal Goktas (1), Willy Hereman (1) ((1) Colorado School of Mines) | Invariants and Symmetries for Partial Differential Equations and
Lattices | To appear in Proceedings of Fourth International Conference on
Mathematical and Numerical Aspects of Wave Propagation (June 1-5, 1998,
Golden, CO), 5 pages, Latex, uses the style file proc209.sty | null | null | null | solv-int nlin.SI | null | Methods for the computation of invariants and symmetries of nonlinear
evolution, wave, and lattice equations are presented. The algorithms are based
on dimensional analysis, and can be implemented in any symbolic language, such
as Mathematica. Invariants and symmetries are shown for several well-known
equations.
Our Mathematica package allows one to automatically compute invariants and
symmetries. Applied to systems with parameters, the package determines the
conditions on these parameters so that a sequence of invariants or symmetries
exists. The software can thus be used to test the integrability of model
equations for wave phenomena.
| [
{
"version": "v1",
"created": "Mon, 26 Jan 1998 16:20:48 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Goktas",
"Unal",
"",
"Colorado School of Mines"
],
[
"Hereman",
"Willy",
"",
"Colorado School of Mines"
]
] |
solv-int/9801025 | Myrzakulov Ratbay | G.N.Nugmanova (Centre for Nonlinear Problems, Alma-Ata-35, Kazakstan) | On the Lakshmanan and gauge equivalent counterpart of the
Myrzakulov-VIII equation | 5 pages, Latex, no figures; [email protected] | null | null | null | solv-int nlin.SI | null | The Lakshmanan equivalent counterparts of the some Myrzakulov equations are
found.
| [
{
"version": "v1",
"created": "Tue, 27 Jan 1998 10:05:14 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Nugmanova",
"G. N.",
"",
"Centre for Nonlinear Problems, Alma-Ata-35, Kazakstan"
]
] |
solv-int/9801026 | Yasuhiro Fujii | Yasuhiro Fujii and Miki Wadati | Correlation Functions of Finite XXZ model with Boundaries | 16pages, LaTeX2e file, errors corrected | null | null | null | solv-int cond-mat hep-th nlin.SI | null | The finite XXZ model with boundaries is considered. We use the Matrix Product
Ansatz (MPA), which was originally developed in the studies on the asymmetric
simple exclusion process and the quantum antiferromagnetic spin chain. The MPA
tells that the eigenstate of the Hamiltonian is constructed by the
Zamolodchikov-Faddeev algebra (ZF-algebra) and the boundary states. We adopt
the type I vertex operator of $U_q(\hat{sl}_2)$ as the ZF-algebra and realize
the boundary states in the bosonic $U_q(\hat{sl}_2)$ form. The correlation
functions are given by the product of the vertex operators and the bosonic
boundary states. We express them in the integration forms.
| [
{
"version": "v1",
"created": "Wed, 28 Jan 1998 05:37:34 GMT"
},
{
"version": "v2",
"created": "Fri, 13 Mar 1998 10:15:05 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Fujii",
"Yasuhiro",
""
],
[
"Wadati",
"Miki",
""
]
] |
solv-int/9802001 | Akira Takamura | Akira Takamura, Ken'ichi Takano | Braid Structure and Raising-Lowering Operator Formalism in Sutherland
Model | 11 pages, Latex, no figures | null | 10.1088/0305-4470/31/25/002 | DPNU-98-03 | solv-int cond-mat nlin.SI | null | We algebraically construct the Fock space of the Sutherland model in terms of
the eigenstates of the pseudomomenta as basis vectors. For this purpose, we
derive the raising and lowering operators which increase and decrease
eigenvalues of pseudomomenta. The operators exchanging eigenvalues of two
pseudomomenta have been known. All the eigenstates are systematically produced
by starting from the ground state and multiplying these operators to it.
| [
{
"version": "v1",
"created": "Fri, 30 Jan 1998 01:55:13 GMT"
},
{
"version": "v2",
"created": "Sun, 3 May 1998 06:17:09 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Takamura",
"Akira",
""
],
[
"Takano",
"Ken'ichi",
""
]
] |
solv-int/9802002 | Dionisio Bazeia | D. Bazeia and F. Moraes | Chiral Solitons in Generalized Korteweg-de Vries Equations | 9 pages, latex, no figures. References added, typos corrected | Phys. Lett. A, 249 (1998) 450 | 10.1016/S0375-9601(98)00727-0 | MIT-CTP-2713 | solv-int cond-mat.soft hep-th nlin.SI | null | Generalizations of the Korteweg-de Vries equation are considered, and some
explicit solutions are presented. There are situations where solutions engender
the interesting property of being chiral, that is, of having velocity
determined in terms of the parameters that define the generalized equation,
with a definite sign.
| [
{
"version": "v1",
"created": "Fri, 30 Jan 1998 14:03:21 GMT"
},
{
"version": "v2",
"created": "Thu, 23 Jul 1998 15:09:07 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Bazeia",
"D.",
""
],
[
"Moraes",
"F.",
""
]
] |
solv-int/9802003 | Ziemowit Popowicz | S.Krivonos, A.Pashnev and Z.Popowicz | Lax pairs for N=2,3 Supersymmetric KdV Equations and their Extensions | 8 pages, LaTex | null | 10.1142/S0217732398001510 | IFT UWr 919/98 | solv-int hep-th nlin.SI | null | We present the Lax operator for the N=3 KdV hierarchy and consider its
extensions. We also construct a new infinite family of N=2 supersymmetric
hierarchies by exhibiting the corresponding super Lax operators. The new
realization of N=4 supersymmetry on the two general N=2 superfields, bosonic
spin 1 and fermionic spin 1/2, is discussed.
| [
{
"version": "v1",
"created": "Fri, 30 Jan 1998 16:10:36 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Krivonos",
"S.",
""
],
[
"Pashnev",
"A.",
""
],
[
"Popowicz",
"Z.",
""
]
] |
solv-int/9802004 | null | Unal Goktas (1), Willy Hereman (1) ((1) Colorado School of Mines) | Computation of Higher-order Symmetries for Nonlinear Evolution and
Lattice Equations | Submitted to: Advances in Computational Mathematics, 23 pages, Latex,
uses the style file bal.sty | null | null | null | solv-int nlin.SI | null | A straightforward algorithm for the symbolic computation of higher-order
symmetries of nonlinear evolution equations and lattice equations is presented.
The scaling properties of the evolution or lattice equations are used to
determine the polynomial form of the higher-order symmetries. The coefficients
of the symmetry can be found by solving a linear system. The method applies to
polynomial systems of PDEs of first-order in time and arbitrary order in one
space variable. Likewise, lattices must be of first order in time but may
involve arbitrary shifts in the discretized space variable.
The algorithm is implemented in Mathematica and can be used to test the
integrability of both nonlinear evolution equations and semi-discrete lattice
equations. With our Integrability Package, higher-order symmetries are obtained
for several well-known systems of evolution and lattice equations. For PDEs and
lattices with parameters, the code allows one to determine the conditions on
these parameters so that a sequence of higher-order symmetries exist. The
existence of a sequence of such symmetries is a predictor for integrability.
| [
{
"version": "v1",
"created": "Sat, 31 Jan 1998 00:42:42 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Goktas",
"Unal",
"",
"Colorado School of Mines"
],
[
"Hereman",
"Willy",
"",
"Colorado School of Mines"
]
] |
solv-int/9802005 | YU-Song Ju | Yu Song-Ju, Kouichi Toda and Takeshi Fukuyama | Hierarchy of Higher Dimensional Integrable System | 10 pages, uses ioplppt.sty | null | null | null | solv-int nlin.SI | null | Integrable equations in ($1 + 1$) dimensions have their own higher order
integrable equations, like the KdV, mKdV and NLS hierarchies etc. In this paper
we consider whether integrable equations in ($2 + 1$) dimensions have also the
analogous hierarchies to those in ($1 + 1$) dimensions. Explicitly is discussed
the Bogoyavlenskii-Schiff(BS) equation. For the BS hierarchy, there appears an
ambiguity in the Painlev\'e test. Nevertheless, it may be concluded that the BS
hierarchy is integrable.
| [
{
"version": "v1",
"created": "Tue, 3 Feb 1998 10:36:19 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Song-Ju",
"Yu",
""
],
[
"Toda",
"Kouichi",
""
],
[
"Fukuyama",
"Takeshi",
""
]
] |
solv-int/9802006 | Myrzakulov Ratbay | G.N.Nugmanova (Centre for Nonlinear Problems, Alma-Ata, Kazakstan) | Surfaces, curves and the Lakshmanan equivalent counterparts of the some
Myrzakulov equations | 8 pages, LaTex, no figures, [email protected] | null | null | null | solv-int nlin.SI | null | The Lakshmanan equivalent counterparts of the some Myrzakulov equations are
found.
| [
{
"version": "v1",
"created": "Fri, 6 Feb 1998 11:24:28 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Nugmanova",
"G. N.",
"",
"Centre for Nonlinear Problems, Alma-Ata, Kazakstan"
]
] |
solv-int/9802007 | Dionisio Bazeia | D. Bazeia | Chiral Solutions to Generalized Burgers and Burgers-Huxley Equations | 17 pages, latex, no figures | null | null | MIT-CTP 2714 | solv-int cond-mat.soft hep-th nlin.SI | null | We investigate generalizations of the Burgers and Burgers-Huxley equations.
The investigations we offer focus attention mainly on presenting explict
analytical solutions by means of relating these generalized equations to
relativistic 1+1 dimensional systems of scalar fields where topological
solutions are known to play a role. Emphasis is given on chiral solutions, that
is, on the possibility of finding solutions that travel with velocities
determined in terms of the parameters that identify the generalized equation,
with a definite sign.
| [
{
"version": "v1",
"created": "Fri, 6 Feb 1998 17:08:13 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Bazeia",
"D.",
""
]
] |
solv-int/9802008 | Fis. Teorica. Valladolid. | Angel Ballesteros and Orlando Ragnisco | A systematic construction of completely integrable Hamiltonians from
coalgebras | 26 pages, LaTeX | null | 10.1088/0305-4470/31/16/009 | UBU-Dfis-97-12 | solv-int nlin.SI | null | A universal algorithm to construct N-particle (classical and quantum)
completely integrable Hamiltonian systems from representations of coalgebras
with Casimir element is presented. In particular, this construction shows that
quantum deformations can be interpreted as generating structures for integrable
deformations of Hamiltonian systems with coalgebra symmetry. In order to
illustrate this general method, the $so(2,1)$ algebra and the oscillator
algebra $h_4$ are used to derive new classical integrable systems including a
generalization of Gaudin-Calogero systems and oscillator chains. Quantum
deformations are then used to obtain some explicit integrable deformations of
the previous long-range interacting systems and a (non-coboundary) deformation
of the $(1+1)$ Poincar\'e algebra is shown to provide a new
Ruijsenaars-Schneider-like Hamiltonian.
| [
{
"version": "v1",
"created": "Fri, 6 Feb 1998 17:43:02 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Ballesteros",
"Angel",
""
],
[
"Ragnisco",
"Orlando",
""
]
] |
solv-int/9802009 | Bireswar Basu-Mallick | B. Basu-Mallick | Multi-parameter deformed and nonstandard $Y(gl_M)$ Yangian symmetry in
integrable variants of Haldane-Shastry spin chain | 18 pages, latex, no figures | null | 10.1143/JPSJ.67.2227 | null | solv-int hep-th nlin.SI | null | By using `anyon like' representations of permutation algebra, which pick up
nontrivial phase factors while interchanging the spins of two lattice sites, we
construct some integrable variants of Haldane-Shastry (HS) spin chain. Lax
equations for these spin chains allow us to find out the related conserved
quantities. However, it turns out that such spin chains also possess a few
additional conserved quantities which are apparently not derivable from the Lax
equations. Identifying these additional conserved quantities, and the usual
ones related to Lax equations, with different modes of a monodromy matrix, it
is shown that the above mentioned HS like spin chains exhibit multi-parameter
deformed and `nonstandard' variants of $Y(gl_M)$ Yangian symmetry.
| [
{
"version": "v1",
"created": "Tue, 10 Feb 1998 04:58:00 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Basu-Mallick",
"B.",
""
]
] |
solv-int/9802010 | David H. Sattinger | R. Beals, D. H. Sattinger, and E. Williams | A Dirac Sea and thermodynamic equilibrium for the quantized three-wave
interaction | null | null | 10.1063/1.532306 | null | solv-int nlin.SI | null | The classical version of the three wave interaction models the creation and
destruction of waves; the quantized version models the creation and destruction
of particles. The quantum three wave interaction is described and the Bethe
Ansatz for the eigenfunctions is given in closed form. The Bethe equations are
derived in a rigorous fashion and are shown to have a thermodynamic limit. The
Dirac sea of negative energy states is obtained as the infinite density limit.
Finite particle/hole excitations are determined and the asymptotic relation of
energy and momentum is obtained. The Yang-Yang functional for the relative free
energy of finite density excitations is constructed and is shown to be convex
and bounded below. The equations of thermal equilibrium are obtained.
| [
{
"version": "v1",
"created": "Wed, 11 Feb 1998 23:49:05 GMT"
}
] | 2015-06-26T00:00:00 | [
[
"Beals",
"R.",
""
],
[
"Sattinger",
"D. H.",
""
],
[
"Williams",
"E.",
""
]
] |
solv-int/9802011 | null | Adam Doliwa | Quadratic reductions of quadrilateral lattices | 24 pages | J. Geom. Phys. 30 (1999) 169-186 | 10.1016/S0393-0440(98)00053-9 | null | solv-int nlin.SI | null | It is shown that quadratic constraints are compatible with the geometric
integrability scheme of the multidimensional quadrilateral lattice equation.
The corresponding Ribaucour reduction of the fundamental transformation of
quadrilateral lattices is found as well, and superposition of the Ribaucour
transformations is presented in the vectorial framework. Finally, the quadratic
reduction approach is illustrated on the example of multidimensional circular
lattices.
| [
{
"version": "v1",
"created": "Fri, 13 Feb 1998 14:52:23 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Doliwa",
"Adam",
""
]
] |
solv-int/9802012 | Sergei M. Sergeev | I. G. Korepanov and S. M. Sergeev | Eigenvector and eigenvalue problem for 3D bosonic model | LaTeX, 18 pages | null | null | null | solv-int nlin.SI | null | In this paper we reformulate free field theory models defined on the
rectangular $D+1$ dimensional lattices as $D+1$ evolution models. This
evolution is in part a simple linear evolution on free (``creation'' and
``annihilation'') operators. Formal eigenvectors of this linear evolution can
be directly constructed, and them play the role of the ``physical'' creation
and annihilation operators. These operators being completed by a ``physical''
vacuum vector give the spectrum of the evolution operator, as well as the trace
of the evolution operator give a correct expression for the partition function.
As an example, Bazhanov -- Baxter's free bosonic model is considered.
| [
{
"version": "v1",
"created": "Sat, 14 Feb 1998 12:18:41 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Korepanov",
"I. G.",
""
],
[
"Sergeev",
"S. M.",
""
]
] |
solv-int/9802013 | Francois Delduc | F. delduc, L. Gallot | Supersymmetric Drinfeld-Sokolov reduction | 25 pages, LaTeX file | null | 10.1063/1.532532 | ENSLAPP-L-668/97 | solv-int nlin.SI | null | The Drinfeld-Sokolov construction of integrable hierarchies, as well as its
generalizations, may be extended to the case of loop superalgebras. A
sufficient condition on the algebraic data for the resulting hierarchy to be
invariant under supersymmetry transformation is given. The method used is a
construction of the hierarchies in superspace, where supersymmetry is manifest.
Several examples are discussed.
| [
{
"version": "v1",
"created": "Fri, 20 Feb 1998 14:29:37 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"delduc",
"F.",
""
],
[
"Gallot",
"L.",
""
]
] |
solv-int/9802014 | Sergei M. Sergeev | S. M. Sergeev | 3D symplectic map | LaTeX, 13 pages | null | 10.1016/S0375-9601(99)00072-9 | null | solv-int nlin.SI | null | Quantum 3D R-matrix in the classical (i.e. functional) limit gives a
symplectic map of dynamical variables. The corresponding 3D evolution model is
considered. An auxiliary problem for it is a system of linear equations playing
the role of the monodromy matrix in 2D models. A generating function for the
integrals of motion is constructed as a determinant of the auxiliary system.
| [
{
"version": "v1",
"created": "Sat, 21 Feb 1998 12:31:03 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Sergeev",
"S. M.",
""
]
] |
solv-int/9802015 | Wenli Yang | Bo-yu Hou and Wen-li Yang | The nondynamical r-matrix structure of the elliptic
Ruijsenaars-Schneider model with N=2 | 7 pages, Latex file 17k | Commun.Theor.Phys.33:371-376,2000 | null | IMPNWU-971219 | solv-int nlin.SI | null | We demonstrate that in a certain gauge the elliptic Ruijsenaars-Shneider
model with N=2 admits a nondynamical r-matrix structure and the corresponding
classical r-matrix is the same as that of its non-relativistic counterpart
(Calogero-Moser model) in the same gauge.The relation between our
(classical)Lax operator and the Lax operator given by Ruijsenaars is also
obtained.
| [
{
"version": "v1",
"created": "Sun, 22 Feb 1998 09:24:31 GMT"
}
] | 2008-11-26T00:00:00 | [
[
"Hou",
"Bo-yu",
""
],
[
"Yang",
"Wen-li",
""
]
] |
solv-int/9802016 | Juri Suris | Yuri B. Suris (Bremen/Berlin) and Orlando Ragnisco (Rome) | What is the relativistic Volterra lattice? | 48 pp, LaTeX | Commun. Math. Phys., 1999, V. 200, p. 445--485. | 10.1007/s002200050537 | null | solv-int nlin.SI | null | We develop a systematic procedure of finding integrable ''relativistic''
(regular one-parameter) deformations for integrable lattice systems. Our
procedure is based on the integrable time discretizations and consists of three
steps. First, for a given system one finds a local discretization living in the
same hierarchy. Second, one considers this discretization as a particular
Cauchy problem for a certain 2-dimensional lattice equation, and then looks for
another meaningful Cauchy problems, which can be, in turn, interpreted as new
discrete time systems. Third, one has to identify integrable hierarchies to
which these new discrete time systems belong. These novel hierarchies are
called then ''relativistic'', the small time step $h$ playing the role of
inverse speed of light. We apply this procedure to the Toda lattice (and
recover the well-known relativistic Toda lattice), as well as to the Volterra
lattice and a certain Bogoyavlensky lattice, for which the ''relativistic''
deformations were not known previously.
| [
{
"version": "v1",
"created": "Tue, 24 Feb 1998 14:45:20 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Suris",
"Yuri B.",
"",
"Bremen/Berlin"
],
[
"Ragnisco",
"Orlando",
"",
"Rome"
]
] |
solv-int/9802017 | Myrzakulov Ratbay | R. Myrzakulov | Solitons, Surfaces, Curves, and the Spin Description of Nonlinear
Evolution Equations | 25 pages, LaTex, no figures | null | null | null | solv-int nlin.SI | null | The briefly review on the common spin description of the nonlinear evolution
equations.
| [
{
"version": "v1",
"created": "Thu, 26 Feb 1998 09:24:55 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Myrzakulov",
"R.",
""
]
] |
solv-int/9802018 | Ivanov Evgenyi | E. Ivanov | On gauge-equivalent formulations of N=4 SKdV hierarchy | 7 pages, LaTeX | null | 10.1142/S021773239800303X | null | solv-int hep-th nlin.SI | null | We point out that the N=4 supersymmetric KdV hierarchy, when written through
the prepotentials of the bosonic chiral and antichiral N=2 supercurrents,
exhibits a freedom related to the possibility to choose different gauges for
the prepotentials. In particular, this implies that the Lax operator for the
N=4 SKdV system and the associated realization of N=4 supersymmetry obtained in
solv-int/9802003 are reduced to the previously known ones. We give the
prepotential form of the `small' N=4 superconformal algebra, the second
hamiltonian structure algebra of the N=4 SKdV hierarchy, for two choices of
gauge.
| [
{
"version": "v1",
"created": "Thu, 26 Feb 1998 22:03:55 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Ivanov",
"E.",
""
]
] |
solv-int/9803001 | Metin Gurses | Metin Gurses (Bilkent University) | Motion of Curves on Two Dimensional Surfaces and Soliton Equations | Latex, 15 pp, to be published in Physics Letters A | null | 10.1016/S0375-9601(98)00151-0 | null | solv-int nlin.SI | null | A connection is established between the soliton equations and curves moving
in a three dimensional space $V_{3}$. The sign of the self-interacting terms of
the soliton equations are related to the signature of $V_{3}$. It is shown that
there corresponds a moving curve to each soliton equations.
| [
{
"version": "v1",
"created": "Fri, 27 Feb 1998 14:55:50 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Gurses",
"Metin",
"",
"Bilkent University"
]
] |
solv-int/9803002 | Wen-Xiu Ma | Wen-Xiu MA | Extension of Hereditary Symmetry Operators | 13 pages, LaTex | null | 10.1088/0305-4470/31/35/009 | null | solv-int nlin.SI | null | Two models of candidates for hereditary symmetry operators are proposed and
thus many nonlinear systems of evolution equations possessing infinitely many
commutative symmetries may be generated. Some concrete structures of hereditary
symmetry operators are carefully analyzed on the base of the resulting general
conditions and several corresponding nonlinear systems are explicitly given out
as illustrative examples.
| [
{
"version": "v1",
"created": "Tue, 3 Mar 1998 06:05:54 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"MA",
"Wen-Xiu",
""
]
] |
solv-int/9803003 | Galina Gorbatina | Valery S. Dryuma, Makoto Matsumoto | Finsler-Geometrical Approach to the Studying of Nonlinear Dynamical
Systems | 22 pages, Latex; Reports of Math. Phys.(1998) | null | null | null | solv-int nlin.SI | null | A two dimensional Finsler space associated with the differential equation
$y''=Y_3 y'^3+Y_2 y'^2+Y_1 y'+Y_0$ is characterized by a tensor equation and
called the Douglas space. An application to the Lorenz nonlinear dynamical
equation is discussed from the standpoint of Finsler geometry.
| [
{
"version": "v1",
"created": "Wed, 4 Mar 1998 17:52:11 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Dryuma",
"Valery S.",
""
],
[
"Matsumoto",
"Makoto",
""
]
] |
solv-int/9803004 | Galina Gorbatina | Valery S. Dryuma | On the Law of Transformation of Affine Connection and its Integration.
Part 1. Generalization of the Lame equations | 18 pages, Latex | Buletinul Academiei de Stiinte a Republicii Moldova Matematica,
v.1(26), 1998, p.55-68 | null | null | solv-int nlin.SI | null | The law of transformation of affine connection for n-dimensional manifolds as
the system of nonlinear equations on local coordinates of manifold is
considered. The extension of the Darboux-Lame system of equations to the spaces
of constant negative curvature is demonstrated. Geodesic deviation equation as
well as the equations of geodesics are presented in the form of the matrix
Darboux-Lame system of equations.
| [
{
"version": "v1",
"created": "Wed, 4 Mar 1998 18:03:59 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Dryuma",
"Valery S.",
""
]
] |
solv-int/9803005 | null | Willy Hereman (1), Unal Goktas (1), Michael D. Colagrosso (1), Antonio
J. Miller (2) ((1) Colorado School of Mines, (2) The Pennsylvania State
University) | Algorithmic Integrability Tests for Nonlinear Differential and Lattice
Equations | Submitted to: Computer Physics Communications, Latex, uses the style
files elsart.sty and elsart12.sty | null | 10.1016/S0010-4655(98)00121-0 | null | solv-int nlin.SI | null | Three symbolic algorithms for testing the integrability of polynomial systems
of partial differential and differential-difference equations are presented.
The first algorithm is the well-known Painlev\'e test, which is applicable to
polynomial systems of ordinary and partial differential equations. The second
and third algorithms allow one to explicitly compute polynomial conserved
densities and higher-order symmetries of nonlinear evolution and lattice
equations.
The first algorithm is implemented in the symbolic syntax of both Macsyma and
Mathematica. The second and third algorithms are available in Mathematica. The
codes can be used for computer-aided integrability testing of nonlinear
differential and lattice equations as they occur in various branches of the
sciences and engineering. Applied to systems with parameters, the codes can
determine the conditions on the parameters so that the systems pass the
Painlev\'e test, or admit a sequence of conserved densities or higher-order
symmetries.
| [
{
"version": "v1",
"created": "Fri, 6 Mar 1998 17:31:07 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Hereman",
"Willy",
""
],
[
"Goktas",
"Unal",
""
],
[
"Colagrosso",
"Michael D.",
""
],
[
"Miller",
"Antonio J.",
""
]
] |
solv-int/9803006 | null | Willy Hereman (Colorado School of Mines) | The Painlev\'e Integrability Test | For chapter in book `Computer Algebra in Germany', Eds.: J. Grabmeier
et al. (Springer Verlag, 1998), Submitted to Werner Seiler, March 5, 1998,
Latex | null | null | null | solv-int nlin.SI | null | The Painlev\'e test is a widely applied and quite successful technique to
investigate the integrability of nonlinear ODEs and PDEs by analyzing the
singularity structure of the solutions. The test is named after the French
mathematician Paul Painlev\'e ....
| [
{
"version": "v1",
"created": "Fri, 6 Mar 1998 17:35:45 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Hereman",
"Willy",
"",
"Colorado School of Mines"
]
] |
solv-int/9803007 | pilar Garcia Estevez | J.M. Cervero and P.G. Estevez | Miura Transformation between two Non-Linear Equations in 2+1 dimensions | 14 pages, latex. Journal of Mathematical Physics (to appear) | null | 10.1063/1.532421 | AFTUS-97/15 | solv-int nlin.SI | null | A Dispersive Wave Equation in 2+1 dimensions (2LDW) widely discussed by
different authors is shown to be nothing but the modified version of the
Generalized Dispersive Wave Equation (GLDW). Using Singularity Analysis and
techniques based upon the Painleve Property leading to the Double Singular
Manifold Expansion we shall find the Miura Transformation which converts the
2LDW Equation into the GLDW Equation. Through this Miura Transformation we
shall also present the Lax pair of the 2LDW Equation as well as some
interesting reductions to several already known integrable systems in 1+1
dimensions.
| [
{
"version": "v1",
"created": "Fri, 6 Mar 1998 20:22:30 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Cervero",
"J. M.",
""
],
[
"Estevez",
"P. G.",
""
]
] |
solv-int/9803008 | null | A. N. Leznov | To the Gel'fand-Tsetlin realization of irreducible representations of
classical semisimple algebras | 13 pages, LaTeX | null | null | IIMAS-UNAM No. 77, 1998 | solv-int hep-th math-ph math.MP nlin.SI | null | It is shown that the Gel'fand-Tsetlin realization of irreducible
representations of the $A_n$ algebra is directly connected with a linear
exactly integrable system in the n-dimensional space. General solution for this
system is explicitly given.
| [
{
"version": "v1",
"created": "Sun, 8 Mar 1998 15:10:41 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Leznov",
"A. N.",
""
]
] |
solv-int/9803009 | Wen-Xiu Ma | Wen-Xiu Ma | A Class of Coupled KdV systems and Their Bi-Hamiltonian Formulations | 8 pages, latex | null | 10.1088/0305-4470/31/37/016 | null | solv-int nlin.SI | null | A Hamiltonian pair with arbitrary constants is proposed and thus a sort of
hereditary operators is resulted. All the corresponding systems of evolution
equations possess local bi-Hamiltonian formulation and a special choice of the
systems leads to the KdV hierarchy. Illustrative examples are given.
| [
{
"version": "v1",
"created": "Wed, 11 Mar 1998 04:54:20 GMT"
},
{
"version": "v2",
"created": "Wed, 15 Jul 1998 06:19:31 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Ma",
"Wen-Xiu",
""
]
] |
solv-int/9803010 | Alexander Sorin | V.B. Derjagin, A.N. Leznov and A. Sorin | The solution of the N=(0|2) superconformal f-Toda lattice | 12 pages, latex, no figures, some misprints corrected, one reference
and report-no added | Nucl.Phys. B527 (1998) 643-656 | 10.1016/S0550-3213(98)00368-X | IIMAS-UNAM-80, JINR E2-98-49 | solv-int hep-th nlin.SI | null | The general solution of the two-dimensional integrable generalization of the
f-Toda chain with fixed ends is explicitly presented in terms of matrix
elements of various fundamental representations of the SL(n|n-1) supergroup.
The dominant role of the representation theory of graded Lie algebras in the
problem of constructing integrable mappings and lattices is demonstrated.
| [
{
"version": "v1",
"created": "Thu, 12 Mar 1998 15:59:29 GMT"
},
{
"version": "v2",
"created": "Wed, 25 Mar 1998 15:20:27 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Derjagin",
"V. B.",
""
],
[
"Leznov",
"A. N.",
""
],
[
"Sorin",
"A.",
""
]
] |
solv-int/9803011 | S. Vijayalakshmi | R. Myrzakulov (1), S. Vijayalakshmi (2), R.N. Syzdykova (1) and M.
Lakshmanan(2) ((1) Centre for Nonlinear Dynamics,.Bharathidasan University,
Tiruchirapalli, India (2) Center for Nonlinear Problems, Alma-Ata-35,
Kazakstan) | On the simplest (2+1) dimensional integrable spin systems and their
equivalent nonlinear Schr\"odinger equations | 32 pages, no figures, accepted for publication in J. Math. Phys | J. Math. Phys. vol.39 (1998) 2122-2140 | 10.1063/1.532279 | null | solv-int nlin.SI | null | Using a moving space curve formalism, geometrical as well as gauge
equivalence between a (2+1) dimensional spin equation (M-I equation) and the
(2+1) dimensional nonlinear Schr\"odinger equation (NLSE) originally discovered
by Calogero, discussed then by Zakharov and recently rederived by Strachan,
have been estabilished. A compatible set of three linear equations are obtained
and integrals of motion are discussed. Through stereographic projection, the
M-I equation has been bilinearized and different types of solutions such as
line and curved solitons, breaking solitons, induced dromions, and domain wall
type solutions are presented. Breaking soliton solutions of (2+1) dimensional
NLSE have also been reported. Generalizations of the above spin equation are
discussed.
| [
{
"version": "v1",
"created": "Fri, 13 Mar 1998 07:01:34 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Myrzakulov",
"R.",
""
],
[
"Vijayalakshmi",
"S.",
""
],
[
"Syzdykova",
"R. N.",
""
],
[
"Lakshmanan",
"M.",
""
]
] |
solv-int/9803012 | Sonjiyu Yu | S.J. Yu, K. Toda and T. Fukuyama (Ritsumeikan Univ.) | N-Soliton Solutions to a New (2 + 1) Dimensional Integrable Equation | 7 pages, uses ioplppt.sty | null | 10.1088/0305-4470/31/50/013 | null | solv-int nlin.SI | null | We give explicitly N-soliton solutions of a new (2 + 1) dimensional equation,
$\phi_{xt} + \phi_{xxxz}/4 + \phi_x \phi_{xz} + \phi_{xx} \phi_z/2 +
\partial_x^{-1} \phi_{zzz}/4 = 0$. This equation is obtained by unifying two
directional generalization of the KdV equation, composing the closed ring with
the KP equation and Bogoyavlenskii-Schiff equation. We also find the Miura
transformation which yields the same ring in the corresponding modified
equations.
| [
{
"version": "v1",
"created": "Wed, 18 Mar 1998 07:55:49 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Yu",
"S. J.",
"",
"Ritsumeikan Univ."
],
[
"Toda",
"K.",
"",
"Ritsumeikan Univ."
],
[
"Fukuyama",
"T.",
"",
"Ritsumeikan Univ."
]
] |
solv-int/9803013 | Robert Conte | R. Conte (CEA Saclay) and M. Musette (VUB Brussels) | Towards second order Lax pairs to discrete Painlev\'e equations of first
degree | 16 pages, no figure, standard Latex, to appear in Chaos, solitons and
fractals (1998). Proceedings of Integrability and chaos in discrete systems,
Brussels 2--6 July 1997, eds. I. Antoniou and F. Lambert. Revision (one
reference suppressed) | null | null | S98/018 | solv-int nlin.SI | null | We investigate the question of finding discrete Lax pairs for the six
discrete Painlev\'e equations (Pn). The choice we make is to discretize the
pairs of Garnier, once converted to matricial form.
| [
{
"version": "v1",
"created": "Wed, 18 Mar 1998 10:26:01 GMT"
},
{
"version": "v2",
"created": "Fri, 22 May 1998 16:55:53 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Conte",
"R.",
"",
"CEA Saclay"
],
[
"Musette",
"M.",
"",
"VUB Brussels"
]
] |
solv-int/9803014 | Robert Conte | R. Conte (CEA Saclay) and M. Musette (VUB Brussels) | Rules of discretization for Painlev\'e equations | 21 pages, no figure, standard Latex, to appear in Theory of nonlinear
special functions : the Painlev\'e transcendents, eds. L. Vinet and P.
Winternitz (Springer, Berlin, 1998). Proceedings of Montreal, 13--17 May 1996 | null | null | S96/075 | solv-int nlin.SI | null | The discrete Painlev\'e property is precisely defined, and basic
discretization rules to preserve it are stated. The discrete Painlev\'e test is
enriched with a new method which perturbs the continuum limit and generates
infinitely many no-log conditions. A general, direct method is provided to
search for discrete Lax pairs.
| [
{
"version": "v1",
"created": "Wed, 18 Mar 1998 11:05:23 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Conte",
"R.",
"",
"CEA Saclay"
],
[
"Musette",
"M.",
"",
"VUB Brussels"
]
] |
solv-int/9803015 | Adam Doliwa | Adam Doliwa, Manuel Manas, Luis Martinez Alonso, Elena Medina and
Paolo Maria Santini | Charged Free Fermions, Vertex Operators and Classical Theory of
Conjugate Nets | 28 pages, 3 Postscript figures | J.Phys.A32:1197-1216,1999 | 10.1088/0305-4470/32/7/010 | null | solv-int hep-th math.DG nlin.SI | null | We show that the quantum field theoretical formulation of the $\tau$-function
theory has a geometrical interpretation within the classical transformation
theory of conjugate nets. In particular, we prove that i) the partial charge
transformations preserving the neutral sector are Laplace transformations, ii)
the basic vertex operators are Levy and adjoint Levy transformations and iii)
the diagonal soliton vertex operators generate fundamental transformations. We
also show that the bilinear identity for the multicomponent
Kadomtsev-Petviashvili hierarchy becomes, through a generalized Miwa map, a
bilinear identity for the multidimensional quadrilateral lattice equations.
| [
{
"version": "v1",
"created": "Fri, 20 Mar 1998 13:21:59 GMT"
}
] | 2008-11-26T00:00:00 | [
[
"Doliwa",
"Adam",
""
],
[
"Manas",
"Manuel",
""
],
[
"Alonso",
"Luis Martinez",
""
],
[
"Medina",
"Elena",
""
],
[
"Santini",
"Paolo Maria",
""
]
] |
solv-int/9803016 | Juri Suris | A.I.Bobenko, B.Lorbeer, Yu.B.Suris (TU Berlin) | Integrable discretizations of the Euler top | null | J. Math. Phys., 1998, V. 39, p. 6668-6683. | 10.1063/1.532648 | null | solv-int nlin.SI | null | Discretizations of the Euler top sharing the integrals of motion with the
continuous time system are studied. Those of them which are also Poisson with
respect to the invariant Poisson bracket of the Euler top are characterized.
For all these Poisson discretizations a solution in terms of elliptic functions
is found, allowing a direct comparison with the continuous time case. We
demonstrate that the Veselov--Moser discretization also belongs to our family,
and apply our methods to this particular example.
| [
{
"version": "v1",
"created": "Mon, 23 Mar 1998 17:07:49 GMT"
}
] | 2015-06-26T00:00:00 | [
[
"Bobenko",
"A. I.",
"",
"TU Berlin"
],
[
"Lorbeer",
"B.",
"",
"TU Berlin"
],
[
"Suris",
"Yu. B.",
"",
"TU Berlin"
]
] |
solv-int/9803017 | Ladislav Hlavaty | L. Hlavaty | All generalized SU(2) chiral models have spectral dependent Lax
formulation | 5 pages, Latex2e, no figures | null | null | FJFI-98-3 | solv-int nlin.SI | null | The equations that define the Lax pairs for generalized principal chiral
models can be solved for any nondegenerate bilinear form on $su(2)$. The
solution is dependent on one free variable that can serve as the spectral
parameter.
| [
{
"version": "v1",
"created": "Thu, 26 Mar 1998 08:47:58 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Hlavaty",
"L.",
""
]
] |
solv-int/9804001 | Oleg M. Kiselev | R.R.Gadyl'shin, O.M. Kiselev (Institute of Mathematics, Ufa Science
Centre, Russian Acad. of Sciences) | On lump instability of Davey--Stewartson II equation | Amstex, 9 pages | null | null | null | solv-int nlin.SI | null | We show that lumps (solitons) of the Davey--Stewartson II equation fail under
small perturbations of initial data.
| [
{
"version": "v1",
"created": "Tue, 31 Mar 1998 16:49:37 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Gadyl'shin",
"R. R.",
"",
"Institute of Mathematics, Ufa Science\n Centre, Russian Acad. of Sciences"
],
[
"Kiselev",
"O. M.",
"",
"Institute of Mathematics, Ufa Science\n Centre, Russian Acad. of Sciences"
]
] |
solv-int/9804002 | Nugzar Makhaldiani | N. Makhaldiani (Dubna) | The system of three vortexes of two dimensional ideal hydrodinamics as a
new example of the (integrable) Nambu- Poisson mechanics | LaTeX, 5 pages | null | null | JINR-E2-97-407 | solv-int nlin.SI | null | A Nambu-Poisson formulation of the system of three ordinary differential
equations describing dynamics of three vortexes of the ideal two-dimensional
hydrodynamics is given. The system is integrated by quadratures.
| [
{
"version": "v1",
"created": "Tue, 31 Mar 1998 13:34:19 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Makhaldiani",
"N.",
"",
"Dubna"
]
] |
solv-int/9804003 | Micheline Musette | M. Musette (VUB, Brussels) | Painlev\'e analysis for nonlinear partial differential equations | 61 pages, no figure, standard Latex, to appear in The Painlev\'e
property, one century later, ed. R. Conte, CRM series in mathematical physics
(Springer--Verlag, Berlin, 1998) (Carg\`ese school, 3-22 June 1996) | null | null | null | solv-int nlin.SI | null | The Painlev\'e analysis introduced by Weiss, Tabor and Carnevale (WTC) in
1983 for nonlinear partial differential equations (PDE's) is an extension of
the method initiated by Painlev\'e and Gambier at the beginning of this century
for the classification of algebraic nonlinear differential equations (ODE's)
without movable critical points. In these lectures we explain the WTC method in
its invariant version introduced by Conte in 1989 and its application to
solitonic equations in order to find algorithmically their associated
B\"acklund transformation. A lot of remarkable properties are shared by these
so-called ``integrable'' equations but they are generically no more valid for
equations modelising physical phenomema. Belonging to this second class, some
equations called ``partially integrable'' sometimes keep remnants of
integrability. In that case, the singularity analysis may also be useful for
building closed form analytic solutions, which necessarily % Conte agree with
the singularity structure of the equations. We display the privileged role
played by the Riccati equation and systems of Riccati equations which are
linearisable, as well as the importance of the Weierstrass elliptic function,
for building solitary waves or more elaborate solutions.
| [
{
"version": "v1",
"created": "Tue, 31 Mar 1998 15:25:01 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Musette",
"M.",
"",
"VUB, Brussels"
]
] |
solv-int/9804004 | Craig A. Tracy | Craig A. Tracy and Harold Widom | Correlation Functions, Cluster Functions and Spacing Distributions for
Random Matrices | 22 pages. LaTeX file. Minor correction | J. Statistical Physics 92 (1998), 809-835. | 10.1023/A:1023084324803 | null | solv-int math.SP nlin.SI | null | The usual formulas for the correlation functions in orthogonal and symplectic
matrix models express them as quaternion determinants. From this representation
one can deduce formulas for spacing probabilities in terms of Fredholm
determinants of matrix-valued kernels. The derivations of the various formulas
are somewhat involved. In this article we present a direct approach which leads
immediately to scalar kernels for unitary ensembles and matrix kernels for the
orthogonal and symplectic ensembles, and the representations of the correlation
functions, cluster functions and spacing distributions in terms of them.
| [
{
"version": "v1",
"created": "Thu, 2 Apr 1998 01:24:27 GMT"
},
{
"version": "v2",
"created": "Wed, 10 Jun 1998 22:46:48 GMT"
},
{
"version": "v3",
"created": "Sat, 27 Jun 1998 00:10:58 GMT"
}
] | 2009-07-11T00:00:00 | [
[
"Tracy",
"Craig A.",
""
],
[
"Widom",
"Harold",
""
]
] |
solv-int/9804005 | Harold Widom | Harold Widom (University of California, Santa Cruz) | On the relation between orthogonal, symplectic and unitary matrix
ensembles | 13 pages. LaTeX file. Improved and simplified derivations of results | J.Statist.Phys. 94 (1999) 347-364 | 10.1023/A:1004536018336 | null | solv-int hep-th math.SP nlin.SI | null | For the unitary ensembles of $N\times N$ Hermitian matrices associated with a
weight function $w$ there is a kernel, expressible in terms of the polynomials
orthogonal with respect to the weight function, which plays an important role.
For the orthogonal and symplectic ensembles of Hermitian matrices there are
$2\times2$ matrix kernels, usually constructed using skew-orthogonal
polynomials, which play an analogous role. These matrix kernels are determined
by their upper left-hand entries. We derive formulas expressing these entries
in terms of the scalar kernel for the corresponding unitary ensembles. We also
show that whenever $w'/w$ is a rational function the entries are equal to the
scalar kernel plus some extra terms whose number equals the order of $w'/w$.
General formulas are obtained for these extra terms. We do not use
skew-orthogonal polynomials in the derivations.
| [
{
"version": "v1",
"created": "Fri, 3 Apr 1998 22:54:00 GMT"
},
{
"version": "v2",
"created": "Mon, 11 May 1998 19:52:14 GMT"
},
{
"version": "v3",
"created": "Thu, 25 Jun 1998 23:17:31 GMT"
},
{
"version": "v4",
"created": "Fri, 17 Jul 1998 22:03:52 GMT"
}
] | 2015-06-26T00:00:00 | [
[
"Widom",
"Harold",
"",
"University of California, Santa Cruz"
]
] |
solv-int/9804006 | John Harnad | J. Harnad and J. McKay (C.R.M., U. de Montreal and Concordia U.) | Modular Solutions to Equations of Generalized Halphen Type | PlainTeX 36gs. (Formula for Hecke operator corrected.) | Proc.Roy.Soc.Lond. 456 (2000) 261-294 | 10.1098/rspa.2000.0517 | CRM 2536 (1998) | solv-int hep-th math-ph math.MP math.QA nlin.SI | null | Solutions to a class of differential systems that generalize the Halphen
system are determined in terms of automorphic functions whose groups are
commensurable with the modular group. These functions all uniformize Riemann
surfaces of genus zero and have $q$--series with integral coefficients.
Rational maps relating these functions are derived, implying subgroup relations
between their automorphism groups, as well as symmetrization maps relating the
associated differential systems.
| [
{
"version": "v1",
"created": "Thu, 9 Apr 1998 12:26:14 GMT"
},
{
"version": "v2",
"created": "Thu, 16 Apr 1998 18:48:45 GMT"
},
{
"version": "v3",
"created": "Tue, 28 Apr 1998 20:52:49 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Harnad",
"J.",
"",
"C.R.M., U. de Montreal and Concordia U."
],
[
"McKay",
"J.",
"",
"C.R.M., U. de Montreal and Concordia U."
]
] |
solv-int/9804007 | Edwin Langmann | Jonas Blom and Edwin Langmann | Novel integrable spin-particle models from gauge theories on a cylinder | 12 pages, LaTex | Phys. Lett. B, 429 (1998) 336-342 | 10.1016/S0370-2693(98)00505-X | null | solv-int hep-th nlin.SI | null | We find and solve a large class of integrable dynamical systems which
includes Calogero-Sutherland models and various novel generalizations thereof.
In general they describe $N$ interacting particles moving on a circle and
coupled to an arbitrary number, $m$, of $su(N)$ spin degrees of freedom with
interactions which depend on arbitrary real parameters $x_j$, $j=1,2,...,m$. We
derive these models from SU(N) Yang-Mills gauge theory coupled to non-dynamic
matter and on spacetime which is a cylinder. This relation to gauge theories is
used to prove integrability, to construct conservation laws, and solve these
models.
| [
{
"version": "v1",
"created": "Wed, 8 Apr 1998 12:04:18 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Blom",
"Jonas",
""
],
[
"Langmann",
"Edwin",
""
]
] |
solv-int/9804008 | Robert Conte | J. Springael (VUB Brussels), R. Conte (CEA Saclay), M. Musette (VUB
Brussels) | On the exact solutions of the Bianchi IX cosmological model in the
proper time | 8 pages, no figure, standard Latex, to appear in Regular and chaotic
dynamics (1998) | null | null | null | solv-int nlin.SI | null | It has recently been argued that there might exist a four-parameter analytic
solution to the Bianchi IX cosmological model, which would extend the
three-parameter solution of Belinskii et al. to one more arbitrary constant. We
perform the perturbative Painlev\'e test in the proper time variable, and
confirm the possible existence of such an extension.
| [
{
"version": "v1",
"created": "Wed, 8 Apr 1998 13:37:45 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Springael",
"J.",
"",
"VUB Brussels"
],
[
"Conte",
"R.",
"",
"CEA Saclay"
],
[
"Musette",
"M.",
"",
"VUB\n Brussels"
]
] |
solv-int/9804009 | null | Masato Hisakado | The Davey Stewartson system and the B\"{a}cklund Transformations | 13 pages, LaTeX | null | 10.1143/JPSJ.67.3038 | null | solv-int hep-th nlin.SI | null | We consider the (coupled) Davey-Stewartson (DS) system and its B\"{a}cklund
transformations (BT). Relations among the DS system, the double
Kadomtsev-Petviashvili (KP) system and the Ablowitz-Ladik hierarchy (ALH) are
established. The DS hierarchy and the double KP system are equivalent. The ALH
is the BT of the DS system in a certain reduction. {From} the BT of coupled DS
system we can obtain new coupled derivative nonlinear Schr\"{o}dinger
equations.
| [
{
"version": "v1",
"created": "Thu, 9 Apr 1998 12:37:40 GMT"
},
{
"version": "v2",
"created": "Tue, 14 Apr 1998 08:40:39 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Hisakado",
"Masato",
""
]
] |
solv-int/9804010 | Osamu Tsuchiya | O. Tsuchiya (University of Tokyo, Komaba) | Determinant formula for the six-vertex model with reflecting end | 10 pages | null | 10.1063/1.532606 | UT-Komaba 98-5 | solv-int nlin.SI | null | Using the Quantum Inverse Scattering Method for the XXZ model with open
boundary conditions, we obtained the determinant formula for the six vertex
model with reflecting end.
| [
{
"version": "v1",
"created": "Fri, 10 Apr 1998 07:27:10 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Tsuchiya",
"O.",
"",
"University of Tokyo, Komaba"
]
] |
solv-int/9804011 | Basil Grammaticos | B. Grammaticos, A. Ramani and S. Lafortune | The Gambier Mapping, Revisited | 11 pages, no figures, to be published in Physica A | Physica A 253, 260-270 (1998) | 10.1016/S0378-4371(97)00675-4 | GMPIB-225 | solv-int nlin.SI | null | We examine critically the Gambier equation and show that it is the generic
linearisable equation containing, as reductions, all the second-order equations
which are integrable through linearisation. We then introduce the general
discrete form of this equation, the Gambier mapping, and present conditions for
its integrability. Finally, we obtain the reductions of the Gambier mapping,
identify their integrable forms and compute their continuous limits.
| [
{
"version": "v1",
"created": "Fri, 10 Apr 1998 14:12:35 GMT"
}
] | 2015-06-26T00:00:00 | [
[
"Grammaticos",
"B.",
""
],
[
"Ramani",
"A.",
""
],
[
"Lafortune",
"S.",
""
]
] |
solv-int/9804012 | Basil Grammaticos | A.Ramani, B.Grammaticos and S.Lafortune | Again, Linearizable Mappings | 14 pages, no figures, to be published in Physica A | Physica A 252, 138-150 (1998) | 10.1016/S0378-4371(97)00614-6 | GMPIB-222 | solv-int nlin.SI | null | We examine a family of 3-point mappings that include mappings solvable
through linearization. The different origins of mappings of this type are
examined: projective equations and Gambier systems. The integrable cases are
obtained through the application of the singularity confinement criterion and
are explicitly integrated.
| [
{
"version": "v1",
"created": "Fri, 10 Apr 1998 14:25:53 GMT"
}
] | 2015-06-26T00:00:00 | [
[
"Ramani",
"A.",
""
],
[
"Grammaticos",
"B.",
""
],
[
"Lafortune",
"S.",
""
]
] |
solv-int/9804013 | Arthur Vartanian | A. H. Vartanian | Higher Order Asymptotics of the Modified Non-Linear Schr\"{o}dinger
Equation | 54 pages, 7 figures, LaTeX, long appendix | null | null | null | solv-int nlin.SI | null | Using the matrix Riemann-Hilbert factorisation approach for non-linear
evolution systems which take the form of Lax-pair isospectral deformations, the
higher order asymptotics as $t \to \pm \infty$ $(x/t \sim {\cal O}(1))$ of the
solution to the Cauchy problem for the modified non-linear Schr\"{o}dinger
equation, $i \partial_{t} u + {1/2} \partial_{x}^{2} u + | u |^{2} u + i s
\partial_{x} (| u |^{2} u) = 0$, $s \in \Bbb R_{> 0}$, which is a model for
non-linear pulse propagation in optical fibres in the subpicosecond time scale,
are obtained: also derived are analogous results for two gauge-equivalent
non-linear evolution equations; in particular, the derivative non-linear
Schr\"{o}dinger equation, $i \partial_{t} q + \partial_{x}^{2} q - i
\partial_{x}(| q |^{2} q) = 0$.
| [
{
"version": "v1",
"created": "Sun, 12 Apr 1998 10:25:47 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Vartanian",
"A. H.",
""
]
] |
solv-int/9804014 | null | A. N. Leznov | The Gel'fand-Tsetlin Selection Rules and Representations of Quantum
Algebras | 16 pages, LaTeX | null | null | IIMAS-UNAM No. 79, 1998 | solv-int hep-th math-ph math.MP math.QA nlin.SI | null | The problem of construction of irreducible representations of quantum $A^q_n$
algebras is solved at the level of explicit integration of the linear
(inhomogeneous) system in finite differences in the n-dimensional space. The
general solution of this system is given explicitly and particular ones, which
correspond to the irreducible representations are selected.
| [
{
"version": "v1",
"created": "Mon, 13 Apr 1998 15:47:08 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Leznov",
"A. N.",
""
]
] |
solv-int/9804015 | Antonio L. Santos | H. Babujian, A. Lima-Santos and R. H. Poghossian | Knizhnik-Zamolodchikov-Bernard equations connected with the eight-vertex
model | 20 pages latex, macro: tcilatex | Int. Journ. Mod. Phys. A14 (1999) 615-630 | 10.1142/S0217751X99000300 | UFSCAR-98-04 | solv-int cond-mat.stat-mech hep-th nlin.SI | null | Using quasiclassical limit of Baxter's 8 - vertex R - matrix, an elliptic
generalization of the Knizhnik-Zamolodchikov equation is constructed. Via
Off-Shell Bethe ansatz an integrable representation for this equation is
obtained. It is shown that there exists a gauge transformation connecting this
equation with Knizhnik-Zamolodchikov-Bernard equation for SU(2)-WZNW model on
torus.
| [
{
"version": "v1",
"created": "Wed, 15 Apr 1998 14:21:37 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Babujian",
"H.",
""
],
[
"Lima-Santos",
"A.",
""
],
[
"Poghossian",
"R. H.",
""
]
] |
solv-int/9804016 | Igor Krichever | I.M. Krichever | Elliptic solutions to difference non-linear equations and nested Bethe
ansatz equations | 21 pages, Latex, no figures | null | null | null | solv-int hep-th nlin.SI | null | We outline an approach to a theory of various generalizations of the elliptic
Calogero-Moser (CM) and Ruijsenaars-Shneider (RS) systems based on a special
inverse problem for linear operators with elliptic coefficients. Hamiltonian
theory of such systems is developed with the help of the universal symplectic
structure proposed by D.H. Phong and the author. Canonically conjugated
action-angle variables for spin generalizations of the elliptic CM and RS
systems are found.
| [
{
"version": "v1",
"created": "Wed, 15 Apr 1998 19:28:43 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Krichever",
"I. M.",
""
]
] |
solv-int/9804017 | Ernesto Raposo | D. Bazeia (Center for Theoretical Physics, Laboratory for Nuclear
Science and Department of Physics, Massachusetts Institute of Technology,
Cambridge MA, USA, and Departamento de Fisica, Universidade Federal da
Paraiba,Joao Pessoa PB, Brazil) and E.P. Raposo (Lyman Laboratory of Physics,
Harvard University, Cambridge MA, USA) | Travelling Wave Solutions in Nonlinear Diffusive and Dispersive Media | 10 pages, Latex | null | null | MIT-CTP-2734 | solv-int cond-mat hep-th nlin.SI | null | We investigate the presence of soliton solutions in some classes of nonlinear
partial differential equations, namely generalized Korteweg-de Vries-Burgers,
Korteveg-de Vries-Huxley, and Korteveg-de Vries-Burgers-Huxley equations, which
combine effects of diffusion, dispersion, and nonlinearity. We emphasize the
chiral behavior of the travelling solutions, whose velocities are determined by
the parameters that define the equation. For some appropriate choices, we show
that these equations can be mapped onto equations of motion of relativistic 1+1
dimensional phi^{4} and phi^{6} field theories of real scalar fields. We also
study systems of two coupled nonlinear equations of the types mentioned.
| [
{
"version": "v1",
"created": "Sat, 25 Apr 1998 14:11:44 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Bazeia",
"D.",
"",
"Center for Theoretical Physics, Laboratory for Nuclear\n Science and Department of Physics, Massachusetts Institute of Technology,\n Cambridge MA, USA, and Departamento de Fisica, Universidade Federal da\n Paraiba,Joao Pessoa PB, Brazil"
],
[
"Raposo",
"E. P.",
"",
"Lyman Laboratory of Physics,\n Harvard University, Cambridge MA, USA"
]
] |
solv-int/9804018 | A. Khare | Bishwajyoti Dey and Avinash Khare | On The Stability of the Compacton Solutions | 9 pages, revtex style, no figures | Phys.Rev. E58 (1998) 2741-2744 | 10.1103/PhysRevE.58.R2741 | IP-BBSR/98-15 | solv-int cond-mat hep-th nlin.SI quant-ph | null | The stability of the recently discovered compacton solutions is studied by
means of both linear stability analysis as well as Lyapunov stability criteria.
From the results obtained it follows that, unlike solitons, all the allowed
compacton solutions are stable, as the stability condition is satisfied for
arbitrary values of the nonlinearity parameter. The results are shown to be
true even for the higher order nonlinear dispersion equations for compactons.
Some new conservation laws for the higher order nonlinear dispersion equations
are also presented.
| [
{
"version": "v1",
"created": "Sat, 25 Apr 1998 18:18:21 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Dey",
"Bishwajyoti",
""
],
[
"Khare",
"Avinash",
""
]
] |
solv-int/9804019 | Nikita A. Slavnov | N. A. Slavnov (Steklov Mathematical Institute, Moscow, Russia) | A nonlinear indentity for the scattering phase of integrable models | 5 pages, Latex, no figures | null | 10.1007/BF02557143 | MI-98-27 | solv-int nlin.SI | null | A nonlinear identity for the scattering phase of quantum integrable models is
proved.
| [
{
"version": "v1",
"created": "Tue, 28 Apr 1998 09:08:57 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Slavnov",
"N. A.",
"",
"Steklov Mathematical Institute, Moscow, Russia"
]
] |
solv-int/9805001 | Satoru Saito | Katsuhiko Yoshida and Satoru Saito | Analytical Study of the Julia Set of a Coupled Generalized Logistic Map | 30pages, 22figures | null | 10.1143/JPSJ.68.1513 | TMUP-HEL-9806 | solv-int nlin.SI | null | A coupled system of two generalized logistic maps is studied. In particular
influence of the coupling to the behaviour of the Julia set in two dimensional
complex space is analyzed both analytically and numerically. It is proved
analytically that the Julia set disappears from the complex plane uniformly as
a parameter interpolates from the chaotic phase to the integrable phase, if the
coupling strength satisfies a certain condition.
| [
{
"version": "v1",
"created": "Sat, 2 May 1998 07:36:10 GMT"
},
{
"version": "v2",
"created": "Sat, 17 Oct 1998 10:35:36 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Yoshida",
"Katsuhiko",
""
],
[
"Saito",
"Satoru",
""
]
] |
solv-int/9805002 | Ming-Hsien Tu | Jiin-Chang Shaw and Ming-Hsien Tu | On the Miura and Backlund transformations associated with the
supersymmetric Gelfand-Dickey bracket | 8 pages, Revtex, version to appear on Mod. Phys. Lett. A | Mod. Phys. Lett. A13 (1998) 979 | 10.1142/S0217732398001054 | null | solv-int nlin.SI | null | The supersymmetric version of the Miura and B\"acklund transformations
associated with the supersymmetric Gelfand-Dickey bracket are investigated from
the point of view of the Kupershmidt-Wilson theorem.
| [
{
"version": "v1",
"created": "Thu, 7 May 1998 12:26:20 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Shaw",
"Jiin-Chang",
""
],
[
"Tu",
"Ming-Hsien",
""
]
] |
solv-int/9805003 | Alexander Turbiner | Alexander Turbiner | Hidden Algebra of Three-Body Integrable Systems | 11 pages, AMS-LaTeX, no figures, minor typos corrected, to appear in
Mod.Phys.Lett.A | Modern Physics Letters A, 13(1998)1473-1483 | 10.1142/S0217732398001558 | Minneapolis TPI-MINN-98/04 and M\'exico ICN-UNAM 98-02 | solv-int cond-mat.stat-mech hep-th math-ph math.MP math.RT math.SP nlin.SI | null | It is shown that all 3-body quantal integrable systems that emerge in the
Hamiltonian reduction method possess the same hidden algebraic structure. All
of them are given by a second degree polynomial in generators of an
infinite-dimensional Lie algebra of differential operators. It leads to new
families of the orthogonal polynomials in two variables.
| [
{
"version": "v1",
"created": "Fri, 8 May 1998 17:07:38 GMT"
},
{
"version": "v2",
"created": "Wed, 3 Jun 1998 14:10:25 GMT"
}
] | 2016-09-08T00:00:00 | [
[
"Turbiner",
"Alexander",
""
]
] |
solv-int/9805004 | Fis. Teorica. Valladolid. | Angel Ballesteros and Francisco J. Herranz | Long range integrable oscillator chains from quantum algebras | 17 pages, LaTeX | null | null | UBU-Dfis-98-01 | solv-int math.QA nlin.SI | null | Completely integrable Hamiltonians defining classical mechanical systems of
$N$ coupled oscillators are obtained from Poisson realizations of
Heisenberg--Weyl, harmonic oscillator and $sl(2,\R)$ coalgebras. Various
completely integrable deformations of such systems are constructed by
considering quantum deformations of these algebras. Explicit expressions for
all the deformed Hamiltonians and constants of motion are given, and the
long-range nature of the interactions is shown to be linked to the underlying
coalgebra structure. The relationship between oscillator systems induced from
the $sl(2,\R)$ coalgebra and angular momentum chains is presented, and a
non-standard integrable deformation of the hyperbolic Gaudin system is
obtained.
| [
{
"version": "v1",
"created": "Fri, 8 May 1998 18:24:25 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Ballesteros",
"Angel",
""
],
[
"Herranz",
"Francisco J.",
""
]
] |
solv-int/9805005 | Manuel Manas | Q. P. Liu and M. Manas | Reduced Vectorial Ribaucour Transformation for the Darboux-Egoroff
Equations | 15 pages LaTeX2e with AMSLaTeX and Babel packages | null | null | null | solv-int math-ph math.DG math.MP nlin.SI | null | The vectorial fundamental transformation for the Darboux equations is reduced
to the symmetric case. This is combined with the orthogonal reduction of Lame
type to obtain those vectorial Ribaucour transformations which preserve the
Egoroff reduction. We also show that a permutability property holds for all
these transformations. Finally, as an example, we apply these transformations
to the Cartesian background.
| [
{
"version": "v1",
"created": "Mon, 11 May 1998 13:33:42 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Liu",
"Q. P.",
""
],
[
"Manas",
"M.",
""
]
] |
solv-int/9805006 | Henrik Aratyn | H. Aratyn | On Grassmannian Description of the Constrained KP Hierarchy | LaTeX, 17 pgs | null | 10.1016/S0393-0440(98)00062-X | null | solv-int nlin.SI | null | This note develops an explicit construction of the constrained KP hierarchy
within the Sato Grassmannian framework. Useful relations are established
between the kernel elements of the underlying ordinary differential operator
and the eigenfunctions of the associated KP hierarchy as well as between the
related bilinear concomitant and the squared eigenfunction potential.
| [
{
"version": "v1",
"created": "Thu, 14 May 1998 16:55:47 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Aratyn",
"H.",
""
]
] |
solv-int/9805007 | Ziemowit Popowicz | Z.Popowicz | Integrable Extensions of N=2 Supersymmetric KdV Hierarchy Associated
with the Nonuniqueness of the Roots of the Lax operator | 9 pages Latex,e-mail [email protected] | null | 10.1016/S0375-9601(98)00731-2 | null | solv-int nlin.SI | null | We preesent a new supersymmetric integrable extensions of the a=4,N=2 KdV
hierarchy. The root of the supersymmetric Lax operator of the KdV equation is
generalized, by including additional fields. This generalized root generate new
hierarchy of integrable equations, for which we investigate the hamiltonian
structure. In special case our system describes the interaction of the KdV
equation with the two MKdV equations.
| [
{
"version": "v1",
"created": "Tue, 19 May 1998 12:39:15 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Popowicz",
"Z.",
""
]
] |
solv-int/9805008 | Ernesto Raposo | E.P. Raposo (Lyman Laboratory of Physics, Harvard University,
Cambridge MA, USA) and D. Bazeia (Center for Theoretical Physics, Laboratory
for Nuclear Science and Department of Physics, Massachusetts Institute of
Technology, Cambridge MA, USA, and Departamento de Fisica, Universidade
Federal da Paraiba,Joao Pessoa PB, Brazil) | Exact Kink Solitons in the Presence of Diffusion, Dispersion, and
Polynomial Nonlinearity | 11 pages, Latex | null | 10.1016/S0375-9601(99)00067-5 | MIT-CTP-2742 | solv-int cond-mat hep-th nlin.SI | null | We describe exact kink soliton solutions to nonlinear partial differential
equations in the generic form u_{t} + P(u) u_{x} + \nu u_{xx} + \delta u_{xxx}
= A(u), with polynomial functions P(u) and A(u) of u=u(x,t), whose generality
allows the identification with a number of relevant equations in physics. We
emphasize the study of chirality of the solutions, and its relation with
diffusion, dispersion, and nonlinear effects, as well as its dependence on the
parity of the polynomials $P(u)$ and $A(u)$ with respect to the discrete
symmetry $u\to-u$. We analyze two types of kink soliton solutions, which are
also solutions to 1+1 dimensional phi^{4} and phi^{6} field theories.
| [
{
"version": "v1",
"created": "Tue, 19 May 1998 22:27:38 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Raposo",
"E. P.",
"",
"Lyman Laboratory of Physics, Harvard University,\n Cambridge MA, USA"
],
[
"Bazeia",
"D.",
"",
"Center for Theoretical Physics, Laboratory\n for Nuclear Science and Department of Physics, Massachusetts Institute of\n Technology, Cambridge MA, USA, and Departamento de Fisica, Universidade\n Federal da Paraiba,Joao Pessoa PB, Brazil"
]
] |
solv-int/9805009 | Ziad Maassarani | Z. Maassarani (Laval University) | Multiplicity A_m Models | 11 pages, Latex, one figure. Some clarifications added | Eur. Phys. J. B vol. 7 (1999) 627-633 - Erratum: vol. 9 (1999) 371 | null | LAVAL-PHY-20/98 | solv-int cond-mat math.QA nlin.SI | null | Models generalizing the su(2) XX spin-chain were recently introduced. These
XXC models also have an underlying su(2) structure. Their construction method
is shown to generalize to the chains based on the fundamental representations
of the A_m Lie algebras. Integrability of the new models is shown in the
context of the quantum inverse scattering method. Their R-matrix is found and
shown to yield a representation of the Hecke algebra. The diagonalization of
the transfer matrices is carried out using the algebraic Bethe Ansatz. I
comment on eventual generalizations and possible links to reaction-diffusion
processes.
| [
{
"version": "v1",
"created": "Tue, 19 May 1998 23:27:27 GMT"
},
{
"version": "v2",
"created": "Tue, 26 May 1998 20:53:56 GMT"
},
{
"version": "v3",
"created": "Thu, 15 Oct 1998 21:50:36 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Maassarani",
"Z.",
"",
"Laval University"
]
] |
solv-int/9805010 | Manuel Manas | Manuel Manas and Luis Martinez Alonso | From Ramond Fermions to Lame Equations for Orthogonal Curvilinear
Coordinates | 14 pages, LaTeX2e with AMSLaTeX and Babel packages | null | 10.1016/S0370-2693(98)00851-X | null | solv-int hep-th math-ph math.DG math.MP nlin.SI | null | We show how Ramond free neutral Fermi fields lead to a $\tau$-function theory
of BKP type which describes iso-orthogonal deformations of systems of ortogonal
curvilinear coordinates. We also provide a vertex operator representation for
the classical Ribaucour transformation.
| [
{
"version": "v1",
"created": "Wed, 20 May 1998 13:03:26 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Manas",
"Manuel",
""
],
[
"Alonso",
"Luis Martinez",
""
]
] |
solv-int/9805011 | Andrei Kapaev | Andrei A. Kapaev (St.Petersburg Department of Steklov Mathematical
Institute) | Connection formulae for degenerated asymptotic solutions of the fourth
Painleve equation | 39 pages, LaTeX | null | null | null | solv-int nlin.SI | null | All possible 1-parametric classical and transcendent degenerated solutions of
the fourth Painleve equation with the corresponding connection formulae of the
asymptotic parameters are described.
| [
{
"version": "v1",
"created": "Thu, 21 May 1998 11:32:58 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Kapaev",
"Andrei A.",
"",
"St.Petersburg Department of Steklov Mathematical\n Institute"
]
] |
solv-int/9805012 | Sergei Yu. Sakovich | Sergei Yu. Sakovich | On integrability of a (2+1)-dimensional perturbed Kdv equation | null | J. Nonlinear Math. Phys. 5 (1998) 230-233 | 10.2991/jnmp.1998.5.3.1 | null | solv-int math-ph math.AP math.MP nlin.SI | null | A (2+1)-dimensional perturbed KdV equation, recently introduced by W.X. Ma
and B. Fuchssteiner, is proven to pass the Painlev\'e test for integrability
well, and its 4$\times $4 Lax pair with two spectral parameters is found. The
results show that the Painlev\'e classification of coupled KdV equations by A.
Karasu should be revised.
| [
{
"version": "v1",
"created": "Fri, 22 May 1998 08:50:47 GMT"
},
{
"version": "v2",
"created": "Wed, 1 Jul 1998 00:00:00 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Sakovich",
"Sergei Yu.",
""
]
] |
solv-int/9805013 | Robert Milson | R. Milson, D. Richter | Quantization of cohomology in semi-simple Lie algebras | Length: 16 pages. To appear in the Journal of Lie Theory, Volume 8,
#2, 1998 | null | null | null | solv-int math.RT nlin.SI | null | The space of realizations of a finite-dimensional Lie algebra by first order
differential operators is naturally isomorphic to H^1 with coefficients in the
module of functions. The condition that a realization admits a
finite-dimensional invariant subspace of functions seems to act as a kind of
quantization condition on this H^1. It was known that this quantization of
cohomology holds for all realizations on 2-dimensional homogeneous spaces, but
the extent to which quantization of cohomology is true in general was an open
question. The present article presents the first known counter-examples to
quantization of cohomology; it is shown that quantization can fail even if the
Lie algebra is semi-simple, and even if the homogeneous space in question is
compact. A explanation for the quantization phenomenon is given in the case of
semi-simple Lie algebras. It is shown that the set of classes in H^1 that admit
finite-dimensional invariant subspaces is a semigroup that lies inside a
finitely-generated abelian group. In order for this abelian group be a discrete
subset of H^1, i.e. in order for quantization to take place, some extra
conditions on the isotropy subalgebra are required. Two different instances of
such necessary conditions are presented.
| [
{
"version": "v1",
"created": "Sat, 23 May 1998 01:17:41 GMT"
},
{
"version": "v2",
"created": "Fri, 29 May 1998 13:56:53 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Milson",
"R.",
""
],
[
"Richter",
"D.",
""
]
] |
solv-int/9806001 | Manuel Manas | Boris G. Konopelchenko, Luis Martinez Alonso and Elena Medina | Singular sector of the KP hierarchy, $\bar{\partial}$-operators of
non-zero index and associated integrable systems | 45 pages, LaTeX 2.09 with epsf,amstex and amssymb styles | null | null | null | solv-int nlin.SI | null | Integrable hierarchies associated with the singular sector of the KP
hierarchy, or equivalently, with $\dbar$-operators of non-zero index are
studied. They arise as the restriction of the standard KP hierarchy to
submanifols of finite codimension in the space of independent variables. For
higher $\dbar$-index these hierarchies represent themselves families of
multidimensional equations with multidimensional constraints. The
$\dbar$-dressing method is used to construct these hierarchies. Hidden KdV,
Boussinesq and hidden Gelfand-Dikii hierarchies are considered too.
| [
{
"version": "v1",
"created": "Fri, 29 May 1998 10:07:53 GMT"
}
] | 2007-05-23T00:00:00 | [
[
"Konopelchenko",
"Boris G.",
""
],
[
"Alonso",
"Luis Martinez",
""
],
[
"Medina",
"Elena",
""
]
] |
solv-int/9806002 | Gregorio Falqui | Gregorio Falqui (SISSA, Trieste, Italy), Franco Magri (Dip. di
Matematica, Univ. di Milano, Italy), Marco Pedroni (Dip. di Matematica, Univ.
di Genova, Italy) | Bihamiltonian Geometry, Darboux Coverings, and Linearization of the KP
Hierarchy | Latex, 27 pages. To appear in Commun. Math. Phys | null | 10.1007/s002200050452 | SISSA 82/97/FM | solv-int nlin.SI | null | We use ideas of the geometry of bihamiltonian manifolds, developed by
Gel'fand and Zakharevich, to study the KP equations. In this approach they have
the form of local conservation laws, and can be traded for a system of ordinary
differential equations of Riccati type, which we call the Central System. We
show that the latter can be linearized by means of a Darboux covering, and we
use this procedure as an alternative technique to construct rational solutions
of the KP equations.
| [
{
"version": "v1",
"created": "Mon, 1 Jun 1998 16:18:34 GMT"
}
] | 2009-10-31T00:00:00 | [
[
"Falqui",
"Gregorio",
"",
"SISSA, Trieste, Italy"
],
[
"Magri",
"Franco",
"",
"Dip. di\n Matematica, Univ. di Milano, Italy"
],
[
"Pedroni",
"Marco",
"",
"Dip. di Matematica, Univ.\n di Genova, Italy"
]
] |
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