Aspects of Integrability in One and Several Dimensions,

Abstract

The results on Inverse Scattering in multidimensions and on the algebraic properties of equations in 2+1 (i.e. two spatial and one temporal) dimensions should be of particular interest: With respect to algebraic properties of equations in 2+1, the question of finding the recursion operator and the bi-Hamiltonian formulation of these equations has remained open for a rather long time. It was even doubted in the literature if the relevant results in 1+1 could be extended to 2+1. It was recently shown that equations in 2+1 solvable via the Inverse Scattering Transform are bi-Hamiltonian systems. Also given are the recursion and bi-Hamiltonian operators for large classes of equations in 2+1, including the Kadomtsev-Petviashvili (a two dimensional analogue of the Korteweg-deVries) and the Davey-Stewartson (a two dimensional analogue of the nonlinear Schrodinger) equations.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1986
Accession Number
ADA193269

Entities

People

  • A. S. Fokas

Organizations

  • Clarkson University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Analogs
  • Applied Mathematics
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Formulas (Mathematics)
  • Integral Equations
  • Integrals
  • Inverse Problems
  • Inverse Scattering
  • Liouville Equation
  • New York
  • Partial Differential Equations
  • Scattering
  • Two Dimensional
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Theoretical Analysis.