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Exactly Solvable and Integrable Systems papers — page 24

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Method of Squared Eigenfunction Potentials in Integrable Hierarchies of KP Type
The method of squared eigenfunction potentials (SEP) is developed systematically to describe and gain new information about Kadomtsev-Petviashvili (KP) hierarchy and its reductions. Interrelation to…
H. Aratyn, E. Nissimov, S. PachevaJan 24, 1997
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The Yangian Symmetry in the Spin Calogero Model and its Applications
By using the non-symmetric Hermite polynomials and a technique based on the Yangian Gelfand-Zetlin bases, we decompose the space of states of the Calogero model with spin into irreducible Yangian…
Kouichi TakemuraJan 22, 1997
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Some eigenstates for a model associated with solutions of tetrahedron equation
Here we present some eigenstates for a 2+1-dimensional model associated with a solution of the tetrahedron equation. The eigenstates include those "particle-like" (namely one-particle and…
I. G. KorepanovJan 22, 1997
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Twisted Quantum Lax Equations
We give the construction of twisted quantum Lax equations associated with quantum groups. We solve these equations using factorization properties of the corresponding quantum groups. Our construction…
Branislav Jurco, Peter SchuppJan 21, 1997
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The Fourier method for the linearized Davey-Stewartson I equation
The linearized Davey-Stewartson equation with varing coefficients is solved by Fourier method. The approach uses the inverse scattering transform for the Davey-Stewartson equation.
O. M. KiselevJan 20, 1997
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The structures underlying soliton solutions in integrable hierarchies
We point out that a common feature of integrable hierarchies presenting soliton solutions is the existence of some special ``vacuum solutions'' such that the Lax operators evaluated on them,…
Luiz A. FerreiraJan 20, 1997
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Some comments on the bi(tri)-Hamiltonian structure of Generalized AKNS and DNLS hierarchies
We give the correct prescriptions for the terms involving the inverse of the derivative of the delta function, in the Hamiltonian structures of the AKNS and DNLS systems, in order for the Jacobi…
H. S. Blas Achic, L. A. Ferreira, J. F. Gomes et al.Jan 20, 1997
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A note on the integrable discretization of the nonlinear Schrödinger equation
We revisit integrable discretizations for the nonlinear Schrödinger equation due to Ablowitz and Ladik. We demonstrate how their main drawback, the non-locality, can be overcome. Namely, we factorize…
Yuri B. SurisJan 14, 1997
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Separation of variables for the Dn type periodic Toda lattice
We prove separation of variables for the most general (Dn type) periodic Toda lattice with 2x2 Lax matrix. It is achieved by finding proper normalisation for the corresponding Baker-Akhiezer…
Vadim B. KuznetsovJan 14, 1997
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P∞ algebra of KP, free fermions and 2-cocycle in the Lie algebra of pseudodifferential operators
The symmetry algebra P∞ = W∞ H I∞ of integrable systems is defined. As an example the classical Sophus Lie point symmetries of all higher KP equations are obtained.…
A. Yu. Orlov, P. WinternitzJan 13, 1997
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Aspects of Solitons in Affine Integrable Hierarchies
We argue that one of the basic ingredients for the appearance of soliton solutions in integrable hierarchies, is the existence of ``vacuum solutions'' corresponding to Lax operators lying in…
Luiz A. Ferreira, Joaquin Sanchez GuillenJan 10, 1997
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Darboux Transformation for the Manin-Radul Supersymmetric KdV equation
In this paper we present a vectorial Darboux transformation, in terms of ordinary determinants, for the supersymmetric extension of the Korteweg-de Vries equation proposed by Manin and Radul. It is…
Q. P. Liu, M. ManasJan 10, 1997
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Crum Transformations and Wronskian Type Solutions for Supersymmetric KdV equation
Darboux transformation is reconsidered for the supersymmetric KdV system. By iterating the Darboux transformation, a supersymmetric extension of the Crum transformation is obtained for the…
Q. P. Liu, M. ManasJan 10, 1997
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Separation of variables for the Ruijsenaars system
We construct a separation of variables for the classical n-particle Ruijsenaars system (the relativistic analog of the elliptic Calogero-Moser system). The separated coordinates appear as the poles…
V. B. Kuznetsov, F. W. Nijhoff, E. K. SklyaninJan 10, 1997
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Asymptotics of a Class of Solutions to the Cylindrical Toda Equations
The small t asymptotics of a class of solutions to the 2D cylindrical Toda equations is computed. The solutions, qk(t), have the representation qk(t) = log det(I-lambda Kk) - log det(I-lambda…
C. A. Tracy, H. WidomJan 10, 1997
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Painleve equations in terms of entire functions
In these lectures we discuss how the Painleve equations can be written in terms of entire functions, and then in the Hirota bilinear (or multilinear) form. Hirota's method, which has been so…
Jarmo HietarintaDec 30, 1996
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Leading Order Temporal Asymptotics of the Modified Non-Linear Schrodinger Equation: Solitonless Sector
Using the matrix Riemann-Hilbert factorisation approach for non-linear evolution equations (NLEEs) integrable in the sense of the inverse scattering method, we obtain, in the solitonless sector, the…
A. V. Kitaev, A. H. VartanianDec 27, 1996
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Bispectral Operators of Rank 1 and Dual Isomonodromic Deformations
A comparison is made between bispectral operator pairs and dual pairs of isomonodromic deformation equations. Through examples, it is shown how operators belonging to rank one bispectral algebras may…
J. HarnadDec 26, 1996
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Some kernels on a Riemann surface
We discuss certain kernels on a Riemann surface, constructed mainly via Baker Akhiezer functions, and indicate relations to dispersionless theory.
R. CarrollDec 24, 1996
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The Whitham equations revisited
We survey some topics involving the Whitham equations, concentrating on the role of the Baker Akhiezer function in averaging. Some connections to symplectic geometry and Seiberg-Witten theory are…
R. Carroll, J. ChangDec 24, 1996
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Irreducible Representations of an Algebra underlying Hidden Symmetries of a class of Quasi Exactly Solvable Systems of Equations
The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The…
Y. Brihaye, S. Giller, P. Kosinski et al.Dec 20, 1996
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On the two-magnon bound states for the quantum Heisenberg chain with variable range exchange
The spectrum of finite-difference two-magnon operator is investigated for quantum S=1/2 chain with variable range exchange of the form h(j-k) -2a(j-k). It is found that usual bound…
J. Dittrich, V. I. InozemtsevDec 20, 1996
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Multidimensional Quadrilateral Lattices are Integrable
The notion of multidimensional quadrilateral lattice is introduced. It is shown that such a lattice is characterized by a system of integrable discrete nonlinear equations. Different useful…
A. Doliwa, P. M. SantiniDec 19, 1996
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Geometric Discretisation of the Toda System
The Laplace sequence of the discrete conjugate nets is constructed. The invariants of the nets satisfy, in full analogy to the continuous case, the system of difference equations equivalent to the…
A. DoliwaDec 19, 1996
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Difference Operator Approach to the Moyal Quantization and Its Application to Integrable Systems
Inspired by the fact that the Moyal quantization is related with nonlocal operation, I define a difference analogue of vector fields and rephrase quantum description on the phase space. Applying this…
Ryuji KemmokuDec 11, 1996
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