Canonicity of Baecklund transformation: r-matrix approach. IIThis is the second part of the paper devoted to the general proof of canonicity of Baecklund transformation (BT) for a Hamiltonian integrable system governed by SL(2)-invariant r-matrix. Introducing…E. K. Sklyanin·Mar 25, 1999SaveLearn
Canonicity of Baecklund transformation: r-matrix approach. IFor the Hamiltonian integrable systems governed by SL(2)-invariant r-matrix (such as Heisenberg magnet, Toda lattice, nonlinear Schroedinger equation) a general procedure for constructing Baecklund…E. K. Sklyanin·Mar 25, 1999SaveLearn
On the Umemura Polynomials for the Painlevé III equationA determinant expression for the rational solutions of the Painlevé III (P III) equation whose entries are the Laguerre polynomials is given. Degeneration of this determinant expression to…K. Kajiwara, T. Masuda·Mar 24, 1999SaveLearn
A generalization of determinant formulas for the solutions of Painlevé II and XXXIV equationsA generalization of determinant formulas for the classical solutions of Painlevé XXXIV and Painlevé II equations are constructed using the technique of Darboux transformation and Hirota's…K. Kajiwara, T. Masuda·Mar 24, 1999SaveLearn
Integrable semi-discretization of the coupled nonlinear Schrödinger equationsA system of semi-discrete coupled nonlinear Schrödinger equations is studied. To show the complete integrability of the model with multiple components, we extend the discrete version of the inverse…T. Tsuchida, H. Ujino, M. Wadati·Mar 18, 1999SaveLearn
On integrability test for ultradiscrete equationsWe consider an integrability test for ultradiscrete equations based on the singularity confinement analysis for discrete equations. We show how singularity pattern of the test is transformed into…Daisuke Takahashi, Kenji Kajiwara·Mar 15, 1999SaveLearn
Multipeakons and a theorem of StieltjesA closed form of the multi-peakon solutions of the Camassa-Holm equation is found using a theorem of Stieltjes on continued fractions. An explicit formula is obtained for the scattering shifts.R. Beals, D. H. Sattinger, J. Szmigielski·Mar 11, 1999SaveLearn
Bethe ansatz for the three-layer Zamolodchikov modelThis paper is a continuation of our previous work (solv-int/9903001). We obtain two more functional relations for the eigenvalues of the transfer matrices for the sl(3) chiral Potts model at…H. E. Boos, V. V. Mangazeev·Mar 10, 1999SaveLearn
Symmetric random matrices and the Pfaff latticeConsider a symmetric (finite) matrix ensemble, with a certain probability distribution. What is the probability that the spectrum belongs to a certain interval or union of intervals on the real line?…M. Adler, P. van Moerbeke·Mar 8, 1999SaveLearn
Singularity Structure Analysis, Integrability, Solitons and Dromions in (2+1)-Dimensional Zakharov EquationsThe (2+1)-dimensional integrable Zakharov equations and their reductions are consideredR. Myrzakulov·Mar 7, 1999SaveLearn
Integrable vs Nonintegrable Geodesic Soliton BehaviorWe study confined solutions of certain evolutionary partial differential equations (pde) in 1+1 space-time. The pde we study are Lie-Poisson Hamiltonian systems for quadratic Hamiltonians defined on…O. B. Fringer, D. D. Holm·Mar 4, 1999SaveLearn
Integrable mixed vertex models from braid-monoid algebraWe use the braid-monoid algebra to construct integrable mixed vertex models. The transfer matrix of a mixed SU(N) model is diagonalized by nested Bethe ansatz approach.M. J. Martins·Mar 4, 1999SaveLearn
Finite genus solutions for the Ablowitz-Ladik hierarchyThe question of constructing the finite genus quasiperiodic solutions for the Ablowitz-Ladik hierarchy (ALH) is considered by establishing relations between the ALH and the Fay's identity for the…V. E. Vekslerchik·Mar 4, 1999SaveLearn
New Integrable Models from FusionIntegrable multistate or multiflavor/color models were recently introduced. They are generalizations of models corresponding to the defining representations of the Uq(sl(m)) quantum algebras. Here I…Z. Maassarani·Mar 3, 1999SaveLearn
Nambu--Poisson reformulation of the finite dimensional dynamical systemsIn this paper we introduce a system of nonlinear ordinary differential equations which in a particular case reduces to Volterra's system. We found in two simplest cases the complete sets of the…Dumitru Baleanu, Nugzar Makhaldiani·Mar 3, 1999SaveLearn
Functional relations and nested Bethe ansatz for sl(3) chiral Potts model at q2=-1We obtain the functional relations for the eigenvalues of the transfer matrix of the sl(3) chiral Potts model for q2=-1. For the homogeneous model in both directions a solution of these functional…H. E. Boos, V. V. Mangazeev·Mar 1, 1999SaveLearn
Vertex Operator Solutions of 2d Dimensionally Reduced GravityWe apply algebraic and vertex operator techniques to solve two dimensional reduced vacuum Einstein's equations. This leads to explicit expressions for the coefficients of metrics solutions of the…Denis Bernard, Nicolas Regnault·Feb 25, 1999SaveLearn
Discrete analogues of the Liouville equationThe notion of Laplace invariants is transferred to the lattices and discrete equations which are difference analogs of hyperbolic PDE's with two independent variables. The sequence of Laplace…V. E. Adler, S. Ya. Startsev·Feb 23, 1999SaveLearn
Baxter's Q-operator for the homogeneous XXX spin chainApplying the Pasquier-Gaudin procedure we construct the Baxter's Q-operator for the homogeneous XXX model as integral operator in standard representation of SL(2). The connection between…S. E. Derkachov·Feb 19, 1999SaveLearn
Soliton equations in 2+1 dimensions: reductions, bilinearizations and simplest solutionsSoliton equations in 2+1 and their 1+1 = 2+0 reductions are considered.N. K. Bliev, G. N. Nugmanova, R. N. Syzdykova et al.·Feb 18, 1999SaveLearn
Picard-Fuchs Equations, Hauptmoduls and Integrable SystemsThe Schwarzian equations satisfied by certain Hauptmoduls (i.e., uniformizing functions for Riemann surfaces of genus zero) are derived from the Picard-Fuchs equations for families of elliptic curves…J. Harnad·Feb 18, 1999SaveLearn
Modular Invariants and Generalized Halphen SystemsGeneralized Halphen systems are solved in terms of functions that uniformize genus zero Riemann surfaces, with automorphism groups that are commensurable with the modular group. Rational maps…J. Harnad, J. McKay·Feb 17, 1999SaveLearn
Orthonormal Polynomials on the Unit Circle and Spatially Discrete Painlevé II EquationWe consider the polynomials ϕn(z)= κn (zn+ bn-1 zn-1+ >...) orthonormal with respect to the weight (λ (z+ 1/z)) dz/2 πi z on the unit circle in the complex plane. The leading…Chie Bing Wang·Feb 17, 1999SaveLearn
Lax Pair Formulation and Multi-soliton Solution of the Integrable Vector Nonlinear Schrodinger EquationThe integrable vector nonlinear Schrodinger (vector NLS) equation is investigated by using Zakharov-Shabat (ZS) scheme. We get a Lax pair formulation of the vector NLS model. Multi-soliton solution…Freddy P. Zen, Hendry I. Elim·Feb 15, 1999SaveLearn
A critical Ising model on the LabyrinthA zero-field Ising model with ferromagnetic coupling constants on the so-called Labyrinth tiling is investigated. Alternatively, this can be regarded as an Ising model on a square lattice with a…M. Baake, U. Grimm, R. J. Baxter·Feb 12, 1999SaveLearn