The Calogero-Sutherland Model and Polynomials with Prescribed SymmetryThe Schrödinger operators with exchange terms for certain Calogero-Sutherland quantum many body systems have eigenfunctions which factor into the symmetric ground state and a multivariable…T. H. Baker, P. J. Forrester·Sep 26, 1996SaveLearn
N=2 KP and KdV hierarchies in extended superspaceWe give the formulation in extended superspace of an N=2 supersymmetric KP hierarchy using chirality preserving pseudo-differential operators. We obtain two quadratic hamiltonian structures, which…F. Delduc, L. Gallot·Sep 24, 1996SaveLearn
Analytic-bilinear approach to integrable hierarchies. I.Generalized KP hierarchyAnalytic-bilinear approach for construction and study of integrable hierarchies, in particular, the KP hierarchy is discussed. It is based on the generalized Hirota identity. This approach allows to…L. V. Bogdanov, B. G. Konopelchenko·Sep 24, 1996SaveLearn
The Kowalewski top: a new Lax representationThe 2x2 monodromy matrices for the Kowalewski top on the Lie algebras e(3), so(4) and so(3,1) are presented. The corresponding quadratic R-matrix structure is the dynamical deformation of the…A. V. Tsiganov·Sep 20, 1996SaveLearn
Virasoro Symmetry Algebra of Dirac Soliton HierarchyA hierarchy of first-degree time-dependent symmetries is proposed for Dirac soliton hierarchy and their commutator relations with time-dependent symmetries are exhibited. Meantime, a hereditary…Wen-Xiu Ma, Kam-Shun Li·Sep 16, 1996SaveLearn
Application of Uniform Asymptotics to the Second Painlevé TranscendentIn this work we propose a new method for investigating connection problems for the class of nonlinear second-order differential equations known as the Painlevé equations. Such problems can be…A. P. Bassom, P. A. Clarkson, C. K. Law et al.·Sep 13, 1996SaveLearn
Symmetries of a class of Nonlinear Third Order Partial Differential EquationsIn this paper we study symmetry reductions of a class of nonlinear third order partial differential equations ut -εuxxt +2κux= u uxxx +αu ux +βux uxx where ε, κ, α and β are…P. A. Clarkson, E. L. Mansfield, T. J. Priestley·Sep 13, 1996SaveLearn
Quasi-point separation of variables for the Henon-Heiles system and a system with quartic potentialWe examine the problem of integrability of two-dimensional Hamiltonian systems by means of separation of variables. The systematic approach to construction of the special non-pure coordinate…S. Rauch-Wojciechowski, A. V. Tsiganov·Sep 13, 1996SaveLearn
Nonlinear Spectral Characterization of Discrete DataThe explicit analytical expression of the Nonlinear Fourier Transform (NFT) of a finite set of data is provided. Then a simple recursion relation for the NFT is constructed as a function of the…M. Boiti, J. Leon, F. Pempinelli·Sep 9, 1996SaveLearn
Toda lattices with indefinite metric II: Topology of the iso-spectral manifoldsWe consider the iso-spectral real manifolds of tridiagonal Hessenberg matrices with real eigenvalues. The manifolds are described by the iso-spectral flows of indefinite Toda lattice equations…Yuji Kodama, Jian Ye·Aug 30, 1996SaveLearn
Common Algebraic Structure for the Calogero-Sutherland ModelsWe investigate common algebraic structure for the rational and trigonometric Calogero-Sutherland models by using the exchange-operator formalism. We show that the set of the Jack polynomials whose…Saburo Kakei·Aug 27, 1996SaveLearn
Nambu tensors and commuting vector fieldsTakhtajan has recently studied the consistency conditions for Nambu brackets, and suggested that they have to be skew-symmetric, and satisfy Leibnitz rule and the Fundamental Identity (FI, it is a…Jarmo Hietarinta·Aug 27, 1996SaveLearn
Discrete version of the Chazy class III equationWe study the discretisation of the Chazy class III equation by two means: a discrete Painlevé test, and the preservation of a two-parameter solution to the continuous equation. We get that way a best…Simon Labrunie, Robert Conte·Aug 20, 1996SaveLearn
A geometrical method towards first integrals for dynamical systemsWe develop a method, based on Darboux' and Liouville's works, to find first integrals and/or invariant manifolds for a physically relevant class of dynamical systems, without making any…Simon Labrunie, Robert Conte·Aug 20, 1996SaveLearn
On Simplest Hamiltonian SystemsSimple Hamiltonian systems, such as mathematical pendulum or Euler equations for rigid body, are solved without computation. It is nothing but a joke but maybe you will find it nice.P. Severa·Aug 20, 1996SaveLearn
Fusion Hierarchies with Open Boundaries and Exactly Solvable ModelsThe formulation of integrable models with open boundary conditions and the functional relations of fused transfer matrices are discussed. It is shown that finite-size corrections to the transfer…Y-K Zhou·Aug 19, 1996SaveLearn
The Calogero-Sutherland Model and Generalized Classical PolynomialsMultivariable generalizations of the classical Hermite, Laguerre and Jacobi polynomials occur as the polynomial part of the eigenfunctions of certain Schrödinger operators for…T. H. Baker, P. J. Forrester·Aug 12, 1996SaveLearn
Binary Nonlinearization of Lax pairs of Kaup-Newell Soliton HierarchyKaup-Newell soliton hierarchy is derived from a kind of Lax pairs different from the original ones. Binary nonlinearization procedure corresponding to the Bargmann symmetry constraint is carried out…Wen-Xiu Ma, Qing Ding, Wei-Guo Zhang et al.·Aug 6, 1996SaveLearn
Equations with an infinite number of explicit Conservation LawsA large class of first order partial nonlinear differential equations in two independent variables which possess an infinite set of polynomial conservation laws derived from an explicit generating…D. B. Fairlie·Aug 5, 1996SaveLearn
On the dynamics of rational solutions for 1-D generalized Volterra systemThe Hirota bilinear formalism and soliton solutions for a generalized Volterra system is presented. Also, starting from the soliton solutions, we obtain a class of nonsingular rational solutions…A. S. Cârstea·Aug 2, 1996SaveLearn
A Local Asymptotic Analysis of the First Discrete Painlevé Equation as the Discrete Independent Variable Approaches InfinityThe first discrete Painlevé equation (dPI), which appears in a model of quantum gravity, is an integrable nonlinear nonautonomous difference equation which yields the well known first Painlevé…Nalini Joshi·Jul 25, 1996SaveLearn
Gibbs' States for Moser-Calogero PotentialsWe present two independent approaches for computing the thermodynamics for classical particles interacting via the Moser--Calogero potential. Combining the results we propose the form of equation of…K. L. Vaninsky·Jul 23, 1996SaveLearn
The Radius of Convergence and the Well-Posedness of the Painlevé Expansions of the Korteweg-deVries equationIn this paper we obtain explicit lower bounds for the radius of convergence of the Painlevé expansions of the Korteweg-de-Vries equation around a movable singularity manifold S in terms of…Nalini Joshi, Gopala K. Srinivasan·Jul 23, 1996SaveLearn
Some further curiosities from the world of integrable lattice systems and their discretizationsUnexpected relations are found between the Toda lattice, the relativistic Toda lattice and the Bruschi--Ragnisco lattice, as well as between their integrable discretizations.Yuri B. Suris·Jul 19, 1996SaveLearn
A Convexity Theorem in the Scattering Theory for the Dirac OperatorThe Dirac operator enters into zero curvature representation for the cubic nonlinear Schrödinger equation. We introduce and study a conformal map from the upper half-plane of the spectral parameter…K. L. Vaninsky·Jul 16, 1996SaveLearn