Classical skew orthogonal polynomials and random matricesSkew orthogonal polynomials arise in the calculation of the n-point distribution function for the eigenvalues of ensembles of random matrices with orthogonal or symplectic symmetry. In particular,…M. Adler, P. J. Forrester, T. Nagao et al.·Jun 28, 1999SaveLearn
Factorization dynamics and Coxeter-Toda latticesIt is shown that the factorization relation on simple Lie groups with standard Poisson Lie structure restricted to Coxeter symplectic leaves gives an integrable dynamical system. This system can be…Tim Hoffmann, Johannes Kellendonk, Nadja Kutz et al.·Jun 24, 1999SaveLearn
Integrability of the higher-order nonlinear Schroedinger equation revisitedOnly the known integrable cases of the Kodama-Hasegawa higher-order nonlinear Schroedinger equation pass the Painleve test. Recent results of Ghosh and Nandy add no new integrable cases of this…S. Yu. Sakovich·Jun 23, 1999SaveLearn
r-matrices for relativistic deformations of integrable systemsWe include the relativistic lattice KP hierarchy, introduced by Gibbons and Kupershmidt, into the r-matrix framework. An r-matrix account of the nonrelativistic lattice KP hierarchy is also…Yuri B. Suris·Jun 16, 1999SaveLearn
On exact solution of a classical 3D integrable modelWe investigate some classical evolution model in the discrete 2+1 space-time. A map, giving an one-step time evolution, may be derived as the compatibility condition for some systems of linear…Sergei M. Sergeev·Jun 15, 1999SaveLearn
Reduction of bihamiltonian systems and separation of variables: an example from the Boussinesq hierarchyWe discuss the Boussinesq system with t5 stationary, within a general framework for the analysis of stationary flows of n-Gel'fand-Dickey hierarchies. We show how a careful use of its…G. Falqui, F. Magri, G. Tondo·Jun 15, 1999SaveLearn
Paraconformal Structures and Integrable SystemsWe consider some natural connections which arise between right-flat (p, q) paraconformal structures and integrable systems. We find that such systems may be formulated in Lax form, with a "Lax…James D. E. Grant·Jun 15, 1999SaveLearn
On the discrete and continuous Miura Chain associated with the Sixth Painlevé EquationA Miura chain is a (closed) sequence of differential (or difference) equations that are related by Miura or Bäcklund transformations. We describe such a chain for the sixth Painlevé equation (),…F. W. Nijhoff, N. Joshi, A. Hone·Jun 10, 1999SaveLearn
Families of quai-bi-Hamiltonian systems and separabilityIt is shown how to construct an infinite number of families of quasi-bi-Hamiltonian (QBH) systems by means of the constrained flows of soliton equations. Three explicit QBH structures are presented…Yunbo Zeng, Wen-Xiu Ma·Jun 10, 1999SaveLearn
Reflection K-Matrices for 19-Vertex ModelsWe derive and classify all regular solutions of the boundary Yang-Baxter equation for 19-vertex models known as Zamolodchikov-Fateev or A1(1) model, Izergin-Korepin or A2(2) model,…A. Lima-Santos·Jun 8, 1999SaveLearn
Soliton Collisions in the Ion Acoustic Plasma EquationsNumerical experiments involving the interaction of two solitary waves of the ion acoustic plasma equations are described. An exact 2-soliton solution of the relevant KdV equation was fitted to the…Yi Li, D. H. Sattinger·Jun 4, 1999SaveLearn
Multipeakons and the Classical Moment ProblemClassical results of Stieltjes are used to obtain explicit formulas for the peakon-antipeakon solutions of the Camassa-Holm equation. The closed form solution is expressed in terms of the orthogonal…Richard Beals, D. H. Sattinger, J. Szmigielski·Jun 4, 1999SaveLearn
Miura Transformations for Integrable Evolution Equations of the Form ut=uxxx+f(t,x,u,ux,uxx)The paper is withdrawn due to an error in Section 3.2. The remaining of the results are included in the preprint solv-int/9605004.Ayse Humeyra Bilge, Fatma Ozdemir·May 26, 1999SaveLearn
A System with a Recursion Operator but One Higher Local Symmetry of the Form ut=uxxx+f(t,x,u,ux,uxx)We construct a recursion operator for the system (ut,vt)=(u4+v2,1/5 v4), for which only one local symmetry is known and we show that the action of the recursion operator on (ut,vt) is a…Ayse Humeyra Bilge·May 25, 1999SaveLearn
On the explicit solutions of the elliptic Calogero systemLet q1,q2,...,qN be the coordinates of N particles on the circle, interacting with the integrable potential Σj<kN(qj-qk), where is the Weierstrass elliptic function. We…L. Gavrilov, A. Perelomov·May 21, 1999SaveLearn
Nonexistence results for the Korteweg-deVries and Kadomtsev-Petviashvili equationsWe study characteristic Cauchy problems for the Korteweg-deVries (KdV) equation ut=uux+uxxx, and the Kadomtsev-Petviashvili (KP) equation uyy=(uxxx+uux+ut)x with…Nalini Joshi, Johannes A. Petersen, Luke M. Schubert·May 20, 1999SaveLearn
Uq(sln)-analog of the XXZ chain with a boundaryWe study Uq(sln) analog of the XXZ spin chain with a boundary magnetic field h. We construct explicit bosonic formulas of the vacuum vector and the dual vacuum vector with a boundary…H. Furutsu, T. Kojima·May 15, 1999SaveLearn
Magnetization waves in Landau-Lifshitz ModelThe solutions of the Landau-Lifshitz equation with finite-gap behavior at infinity are considered. By means of the inverse scattering method the large-time asymptotics is obtained.R. F. Bikbaev, R. A. Sharipov·May 12, 1999SaveLearn
The continuum limit of sl(N/K) integrable super spin chainsI discuss in this paper the continuum limit of integrable spin chains based on the superalgebras sl(N/K). The general conclusion is that, with the full ``supersymmetry'', none of these models…H. Saleur·May 11, 1999SaveLearn
Coupled nonlinear Schrodinger equations with cubic-quintic nonlinearity: Integrability and soliton interaction in non-Kerr mediaWe propose an integrable system of coupled nonlinear Schrodinger equations with cubic-quintic terms describing the effects of quintic nonlinearity on the ultra-short optical soliton pulse propagation…R. Radhakrishnan, A. Kundu, M. Lakshmanan·May 10, 1999SaveLearn
The KP Hierarchy in Miwa CoordinatesA systematic reformulation of the KP hierarchy by using continuous Miwa variables is presented. Basic quantities and relations are defined and determinantal expressions for Fay's identities are…Boris Konopelchenko, Luis Martinez Alonso·May 7, 1999SaveLearn
New integrable systems of derivative nonlinear Schrödinger equations with multiple componentsThe Lax pair for a derivative nonlinear Schrödinger equation proposed by Chen-Lee-Liu is generalized into matrix form. This gives new types of integrable coupled derivative nonlinear Schrödinger…T. Tsuchida, M. Wadati·May 6, 1999SaveLearn
Solutions of Non-linear Differential and Difference Equations with Superposition FormulasMatrix Riccati equations and other nonlinear ordinary differential equations with superposition formulas are, in the case of constant coefficients, shown to have the same exact solutions as their…Alexander Turbiner, Pavel Winternitz·May 6, 1999SaveLearn
Bethe ansatz solution of the closed anisotropic supersymmetric U model with quantum supersymmetryThe nested algebraic Bethe ansatz is presented for the anisotropic supersymmetric U model maintaining quantum supersymmetry. The Bethe ansatz equations of the model are obtained on a…Katrina Hibberd, Itzhak Roditi, Jon Links et al.·May 3, 1999SaveLearn
From Agmon-Kannai expansion to Korteweg-de Vries hierarchyWe present a new method for computation of the Korteweg-de Vries hierarchy via heat invariants of the 1-dimensional Schrodinger operator. As a result new explicit formulas for the KdV hierarchy are…Iosif Polterovich·Apr 30, 1999SaveLearn