Solution of SRS on the finite intervalThe equations of transient stimulated Raman scattering on the finite interval are solved by the spectral transform method on the semi-line. As the problem has a free end, the pump and Stokes output…J. Leon·Oct 16, 1995SaveLearn
Dispersionful analogues of Benney's equations and N-wave systemsWe recall Krichever's construction of additional flows to Benney's hierarchy, attached to poles at finite distance of the Lax operator. Then we construct a ``dispersionful'' analogue…B. Enriquez, A. Yu. Orlov, V. N. Rubtsov·Oct 11, 1995SaveLearn
On Integrable Doebner-Goldin EquationsWe suggest a method for integrating sub-families of a family of nonlinear Schrödinger equations proposed by H.-D.~Doebner and G.A.~Goldin in the 1+1 dimensional case which have…P. Nattermann, R. Zhdanov·Oct 10, 1995SaveLearn
Peakons, R-Matrix and Toda-LatticeThe integrability of a family of hamiltonian systems, describing in a particular case the motionof N ``peakons" (special solutions of the so-called Camassa-Holm equation) is established in the…O. Ragnisco, M. Bruschi·Sep 28, 1995SaveLearn
Nonlinear Behaviour of Time-Stepping Algorithms for Initial Value ProblemsRecent advances in nonlinear dynamical systems theory provide a new insight into numerical properties of discrete algorithms developed to solve nonlinear initial value problems. Basic features like…S. Sello·Sep 27, 1995SaveLearn
Nonsingularity of the direct scattering transform for the KP-2 equation with real exponentially decaying at infinity potentialWe study the direct spectral transform for the heat equation, associated with the KP-2 equation. We show, that for real nonsingular exponentially decaying at infinity potentials the direct problem is…P. G. Grinevich·Sep 25, 1995SaveLearn
The separability and dynamical r-matrix for the constrained flows of Jaulent-Miodek hierarchyWe show here the separability of Hamilton-Jacobi equation for a hierarchy of integrable Hamiltonian systems obtained from the constrained flows of the Jaulent-Miodek hierarchy. The classical Poisson…Yunbo Zeng·Sep 25, 1995SaveLearn
BiHamiltonian Formulations of the Bateman EquationWe discuss a class of evolution equations equivalent to the simplest Universal Field Equation, the so--called Bateman equation, and show that all of them possess (at least) biHamiltonian structure.…J. A. Mulvey·Sep 21, 1995SaveLearn
On Orthogonal and Symplectic Matrix EnsemblesThe focus of this paper is on the probability, Eβ(0;J), that a set J consisting of a finite union of intervals contains no eigenvalues for the finite N Gaussian Orthogonal (β=1) and Gaussian…Craig A. Tracy, Harold Widom·Sep 17, 1995SaveLearn
Differential substitutions and symmetries of hyperbolic equationsThere are considered differential substitutions of the form v=P(x,u,ux) for which there exists a differential operator H=Σki=0 αi Dix such that the differential substitution…S. Ya. Startsev·Sep 15, 1995SaveLearn
Classical Poisson structures and r-matrices from constrained flowsWe construct the classical Poisson structure and r-matrix for some finite dimensional integrable Hamiltonian systems obtained by constraining the flows of soliton equations in a certain way. This…Yunbo Zeng, Jarmo Hietarinta·Sep 14, 1995SaveLearn
Nonisospectral symmetries of the KdV equation and the corresponding symmetries of the Whitham equationsIn our paper we construct a new infinite family of symmetries of the Whitham equations (averaged Korteveg-de-Vries equation). In contrast with the ordinary hydrodynamic-type flows these symmetries…P. G. Grinevich·Sep 13, 1995SaveLearn
Proofs of Two Conjectures Related to the Thermodynamic Bethe AnsatzWe prove that the solution to a pair of nonlinear integral equations arising in the thermodynamic Bethe Ansatz can be expressed in terms of the resolvent kernel of the linear integral operator with…Craig A. Tracy, Harold Widom·Sep 9, 1995SaveLearn
The relativistic Calogero model in an external fieldRecent results are surveyed regarding the spectrum and eigenfunctions of the inverse square Calogero model with harmonic confinement and its relativistic analogue.J. F. van Diejen·Sep 7, 1995SaveLearn
Hidden symmetry of the quantum Calogero-Moser systemHidden symmetry of the quantum Calogero-Moser system with the inverse-square potential is explicitly demonstrated in algebraic sense. We find the underlying algebra explaining the super-integrability…Vadim B. Kuznetsov·Sep 4, 1995SaveLearn
Symmetry approach in boundary value problemsThe problem of construction of the boundary conditions for nonlinear equations is considered compatible with their higher symmetries. Boundary conditions for the sine-Gordon, Jiber-Shabat and KdV…I. T. Habibullin·Aug 31, 1995SaveLearn
Numerical Studies of Localized Structures on an Uneven Bottom in Two DimensionsThe Davey-Stewartson (DS) equations with a perturbation term are presented by taking a fluid system as an example on an uneven bottom. Stability of dromions, solutions of the DS equations with…Tetsu Yajima, Katsuhiro Nishinari·Aug 30, 1995SaveLearn
Non-Fuchsian extension to the Painlevé testWe consider meromorphic particular solutions of nonlinear ordinary differential equations and perform a perturbation à la Poincaré making their linearized equation non-Fuchsian at the movable…Micheline Musette, Robert Conte·Aug 28, 1995SaveLearn
Separation of variables in the A2 type Jack polynomialsAn integral operator M is constructed performing a separation of variables for the 3-particle quantum Calogero-Sutherland (CS) model. Under the action of M the CS eigenfunctions (Jack polynomials…V. B. Kuznetsov, E. K. Sklyanin·Aug 21, 1995SaveLearn
Integer spin particles necessarily produce half-integer angular momentum in a simple complex and periodic HamiltonianExact wave functions are is derived from an azimuthally periodic a self-consistent quantum Hamiltonian in 2+1 dimensions using both the Klein-Gordon and the Schroedinger equations. It isWe shown…Troy Shinbrot·Aug 10, 1995SaveLearn
Hamiltonian Structures on Coadjoint Orbits of Semidirect Product of G=Diff+(S1) and C∞(S1, R)We consider the semidirect product of diffeomorphisms of the circle D=Diff+(S1) and C∞(S1, R) functions, classify its coadjoint orbits and prove the integrability of…A. Zujewski·Aug 2, 1995SaveLearn
Henon-Heiles Hamiltonian for Coupled Upper-Hybrid and Magnetoacoutic Waves in Magnetized PlasmasWe show that the coupled mode equations for the stationary propagation of upper--hybrid and magnetoacoustic waves in magnetized electron--ion plasmas with negative group dispersion can be exactly…N. N. Rao·Jul 24, 1995SaveLearn
On the integrability of stationary and restricted flows of the KdV hierarchy.A bi--Hamiltonian formulation for stationary flows of the KdV hierarchy is derived in an extended phase space. A map between stationary flows and restricted flows is constructed: in a case it…G. Tondo·Jul 22, 1995SaveLearn
On the new approach to variable separation in the time-dependent Schrödinger equation with two space dimensionsWe suggest an effective approach to separation of variables in the Schrödinger equation with two space variables. Using it we classify inequivalent potentials V(x1,x2) such that the corresponding…Renat Z. Zhdanov, Ihor V. Revenko, Wilhelm I. Fushchych·Jul 20, 1995SaveLearn
Multivariable continuous Hahn and Wilson polynomials related to integrable difference systemsMultivariable generalizations of the continuous Hahn and Wilson polynomials are introduced as eigenfunctions of rational Ruijsenaars type difference systems with an external field.J. F. van Diejen·Jul 19, 1995SaveLearn