Integrable Equations in Multi-Dimensions (2+1) are Bi-Hamiltonian Systems,

Abstract

Given a linear eigenvalue problem find all nonlinear equations that are related to it. Associated with a given eigenvalue problem there exists a hierarchy of infinitely many equations. This hierarchy is generated by a certain linear operator. This operator is the squared eigenfunction operator of the underlying linear eigenvalue problem. The operator generating the KdV hierarchy (i.e. the squared eigenfunction operator of the Schrodinger eigenvalue problem) was found by Lenard. Finding the hierarchy associated with a given equation is equivalent to finding the non-Lie point symmetries of the given equation.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1987
Accession Number
ADA193271

Entities

People

  • A. S. Fokas
  • P. M. Santini

Organizations

  • Clarkson University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algebra
  • Commutators
  • Computer Science
  • Construction
  • Delta Functions
  • Directional
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Hierarchies
  • Integrals
  • Inverse Scattering
  • Mathematics
  • Military Research
  • New York
  • Symmetry
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Linear Algebra