Recursion Operators and Bi-Hamiltonian Structures in Multidimensions 1,
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 bi-Hamiltonian nature of all these equations. Recently the recursion operator and the bi-Hamiltonian formulation of the Kadomtsev-Petviashvili equation was presented as a two spatial dimensional analogue of the Korteweg-deVries equation. Here the general theory associated with recursion operators for bi-Hamiltonian equations is presented in two spatial and one temporal dimensions. An application shows that general classes of equations, which include the Kadomtsev-Petviashvili and the Davey-Stewartson 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1986
- Accession Number
- ADA193326
Entities
People
- A. S. Fokas
- P. M. Santini
Organizations
- Clarkson University