
Accession Number : ADA193326
Title : Recursion Operators and BiHamiltonian Structures in Multidimensions 1,
Corporate Author : CLARKSON UNIV POTSDAM NY INST FOR NONLINEAR STUDIES
Personal Author(s) : Santini, P. M. ; Fokas, A. S.
Report Date : JUL 1986
Pagination or Media Count : 72
Abstract : The algebraic properties of exactly solvable evolution equations in one spatial and one temporal dimensions have been well studied. In particular the factorization of certain operators, called recursion operators, establishes the biHamiltonian nature of all these equations. Recently the recursion operator and the biHamiltonian formulation of the KadomtsevPetviashvili equation was presented as a two spatial dimensional analogue of the KortewegdeVries equation. Here the general theory associated with recursion operators for biHamiltonian equations is presented in two spatial and one temporal dimensions. An application shows that general classes of equations, which include the KadomtsevPetviashvili and the DaveyStewartson equations, possess infinitely many commuting symmetries and infinitely many constants of motion in involution under two distinct Poisson brackets. Furthermore, the relevant recursion operators naturally follow from the underlying isospectral eigenvalue problems.
Descriptors : *RECURSIVE FUNCTIONS, *HAMILTONIAN FUNCTIONS, *OPERATORS(MATHEMATICS), CONSTANTS, EIGENVALUES, EVOLUTION(GENERAL), MOTION, POISSON DENSITY FUNCTIONS, THEORY, NONLINEAR SYSTEMS, SCHRODINGER EQUATION.
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE