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Exactly Solvable and Integrable Systems papers — page 17

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Temperature correlators in the two-component one-dimensional gas
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…
A. G. Izergin, A. G. PronkoJan 3, 1998
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N Soliton Solutions to The Bogoyavlenskii-Schiff Equation and A Quest for The Soliton Solution in (3 + 1) Dimensions
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)…
Yu. S. J, K. Toda, N. Sasa et al.Jan 3, 1998
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A Symmetric Generalization of Linear Bäcklund Transformation associated with the Hirota Bilinear Difference Equation
The Hirota bilinear difference equation is generalized to discrete space of arbitrary dimension. Solutions to the nonlinear difference equations can be obtained via Bäcklund transformation of the…
Nobuhiko Shinzawa, Satoru SaitoDec 31, 1997
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Asymptotics of Solutions to the Modified Nonlinear Schrödinger Equation: Solitons on a Non-Vanishing Continuous Background
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…
A. V. Kitaev, A. H. VartanianDec 27, 1997
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Quadratically integrable geodesic flows on the torus and on the Klein bottle
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…
V. S. MatveevDec 23, 1997
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Sigma Models and Minimal Surfaces
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…
Metin GursesDec 23, 1997
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Transformations of Quadrilateral Lattices
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…
A. Doliwa, P. M. Santini, M. ManasDec 20, 1997
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Toda-Darboux maps and vertex operators
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…
M. Adler, P. van MoerbekeDec 19, 1997
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The solution to the q-KdV equation
Let KdV stand for the Nth Gelfand-Dickey reduction of the KP hierarchy. The purpose of this paper is to show that any KdV solution leads effectively to a solution of the q-approximation of KdV. Two…
M. Adler, E. Horozov, P. van MoerbekeDec 19, 1997
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The Quantum Inverse Scattering Method for Hubbard-like Models
This work is concerned with various aspects of the formulation of the quantum inverse scattering method for the one-dimensional Hubbard model. We first establish the essential tools to solve the…
M. J. Martins, P. B. RamosDec 19, 1997
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A Riemann-Hilbert Problem for an Energy Dependent Schrödinger Operator
consider an inverse scattering problem for Schrödinger operators with energy dependent potentials. The inverse problem is formulated as a Riemann-Hilbert problem on a Riemann surface. A vanishing…
David H. Sattinger, Jacek SzmigielskiDec 19, 1997
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A New ``Dual'' Symmetry Structure of the KP Hierarchy
A new infinite set of commuting additional (``ghost'') symmetries is proposed for the KP-type integrable hierarchy. These symmetries allow for a Lax representation in which they are realized…
H. Aratyn, E. Nissimov, S. PachevaDec 18, 1997
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Canonical gauge equivalences of the sAKNS and sTB hierarchies
We study the gauge transformations between the supersymmetric AKNS (sAKNS) and supersymmetric two-boson (sTB) hierarchies. The Hamiltonian nature of these gauge transformations is investigated, which…
Jiin-Chang Shaw, Ming-Hsien TuDec 18, 1997
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Boundary K-matrices and the Lax pair for 1D open XYZ spin-chain
We analysis the symmetries of the reflection equation for open XYZ model and find their solutions K case by case. In the general open boundary conditions, the Lax pair for open…
Guo-xing Ju, Shi-kun Wang, Ke Wu et al.Dec 16, 1997
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The averaging of Hamiltonian structures in discrete variant of Whitham method
Paper is devoted to the construction of averaging procedure of Hamiltonian structures in discrete Whitham method. The procedure is analogous to Dubrovin-Novikov procedure of averaging of local…
A. Ya. MaltsevDec 13, 1997
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The XXC Models
A class of recently introduced multi-states XX models is generalized to include a deformation parameter. This corresponds to an additional nearest-neighbor CC interaction in the defining quadratic…
Z. MaassaraniDec 11, 1997
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Dynamical Correlation Functions for an Impenetrable Bose gas with open boundary conditions
We study the time and temperature dependent correlation functions for an impenetrable bose gas with open boundary conditions. We derive the Fredholm determinant formulae for the correlation…
T. KojimaDec 10, 1997
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Integrability in 3+1 Dimensions: Relaxing a Tetrahedron Relation
I propose a scheme of constructing classical integrable models in 3+1 discrete dimensions, based on a relaxed version of the problem of factorizing a matrix into the product of four matrices of a…
I. G. KorepanovDec 8, 1997
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The New Identity for the Scattering Matrx of Exactly Solvable Models
We discovered a simple quadratic equation, which relates scattering phases of particles on Fermi surface. We consider one dimensional Bose gas and XXZ Heisenberg spin chain.
V. E. Korepin, N. A. SlavnovDec 4, 1997
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Extended N=2 supersymmetric matrix (1,s)-KdV hierarchies
We propose the Lax operators for N=2 supersymmetric matrix generalization of the bosonic (1,s)-KdV hierarchies. The simplest examples - the N=2 supersymmetric a=4 KdV and a=5/2 Boussinesq hierarchies…
S. Krivonos, A. SorinDec 4, 1997
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The Complex Toda Chains and the Simple Lie Algebras - Solutions and Large Time Asymptotics
The asymptotic regimes of the N-site complex Toda chain (CTC) with fixed ends related to the classical series of simple Lie algebras are classified. It is shown that the CTC models have much richer…
V. S. Gerdjikov, E. G. Evstatiev, R. I. IvanovDec 3, 1997
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The Stackel systems and algebraic curves
We show how the Abel-Jacobi map provides all the principal properties of an ample family of integrable mechanical systems associated to hyperelliptic curves. We prove that derivative of the…
A. V. TsiganovDec 2, 1997
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On the geometry of point-expansions for certain class of differential equations of the second order
Second order ordinary differential equations of the form y'' = P(x,y) + 4 Q(x,y) y' + 6 R(x,y) y'2 + 4 S(x,y) y'3 + L(x,y) y'4 are considered and their point-expansions…
O. N. Mikhailov, R. A. SharipovDec 1, 1997
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Integrable Coupled KdV Systems
We give the conditions for a system of N- coupled Korteweg de Vries(KdV) type of equations to be integrable. Recursion operators of each subclasses are also given. All examples for N=2 are explicitly…
Metin Gurses, Atalay KarasuNov 27, 1997
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Singularity confinement and chaos in discrete systems
We present a number of second order maps, which pass the singularity confinement test commonly used to identify integrable discrete systems, but which nevertheless are non-integrable. As a more…
Jarmo Hietarinta, Claude VialletNov 27, 1997
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