On additional motion invariants of classical Hamiltonian wave systems
type: Item
instance of: scholarly article
title: On additional motion invariants of classical Hamiltonian wave systems
zbMATH Open document ID: 0651.35080
DOI: 10.1016/0167-2789(88)90033-4
author: E. I. Schulman
author: V. E. Zakharov
published in: Physica D
publication date: 1988-01-01T00:00:00Z
review text: It is shown that the existence of an analytic invariant in addition to the natural ones (moment, energy and others) for a classical Hamiltonian wave system leads to the existence of infinitely many such invariants. However this phenomenon reduces a Hamiltonian system to a complete integrable system only if the dispersion law is non-degenerative. Results on degenerative dispersion laws and a factorizing of the S-matrix are presented. Concrete examples of Hamiltonian systems are adduced, for instance \(i\psi_ t-\psi_{xx}+\psi_{yy}=| \psi |^ 2\psi.\) Also the singular elements of the scattering matrix are considered.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35P25
zbMATH DE Number: 4061812
zbMATH Keywords: existence
zbMATH Keywords: analytic invariant
zbMATH Keywords: Hamiltonian wave system
zbMATH Keywords: integrable system
zbMATH Keywords: dispersion law
zbMATH Keywords: factorizing
zbMATH Keywords: singular elements
zbMATH Keywords: scattering matrix
MaRDI profile type: Publication
full work available at URL: 0167-2789(88)90033-4
OpenAlex ID: W2051694255
cites work: Method for Solving the Korteweg-deVries Equation
cites work: Canonically conjugate variables for the Korteweg-de Vries equation and the Toda lattice with periodic boundary conditions.
cites work: Q3217024
cites work: Prolongation structures of nonlinear evolution equations
cites work: Prolongation structures of nonlinear evolution equations. II
cites work: A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
cites work: The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
cites work: Korteweg‐devries equation and generalizations. VI. methods for exact solution
cites work: Q4045062
cites work: Q3732104
cites work: Q5621188
cites work: Q4137529
cites work: The solution of the general initial value problem for the full three dimensional three-wave resonant interaction
cites work: On three-dimensional packets of surface waves
cites work: On the soliton solutions of the Davey-Stewartson equation for long waves
cites work: Degenerative dispersion laws, motion invariants and kinetic equations
cites work: To the integrability of the system of two coupled nonlinear Schrödinger equations
cites work: On the integrability of equations of Davey-Stewartson type
cites work: On the propagation of a three-dimensional packet of weakly nonlinear internal gravity waves
cites work: Continual classical Heisenberg models defined on graded su(2,1) and su(3) algebras
cites work: Q3792301
cites work: On the theory of recursion operator
description: scientific article; zbMATH DE number 4061812