Five-wave classical scattering matrix and integrable equations

Vladimir E Zakharov, A. V. Odesskii, M. Cisternino, M. Onorato

Research output: Contribution to journalArticle

Abstract

We study the five-wave classical scattering matrix for nonlinear and dispersive Hamiltonian equations with a nonlinearity of the type u∂u/∂x. Our aim is to find the most general nontrivial form of the dispersion relation ω(k) for which the five-wave interaction scattering matrix is identically zero on the resonance manifold. As could be expected, the matrix in one dimension is zero for the Korteweg-de Vries equation, the Benjamin-Ono equation, and the intermediate long-wave equation. In two dimensions, we find a new equation that satisfies our requirement.

Original languageEnglish (US)
Pages (from-to)759-764
Number of pages6
JournalTheoretical and Mathematical Physics
Volume180
Issue number1
DOIs
StatePublished - 2014

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Integrable Equation
Scattering Matrix
S matrix theory
Matrix Equation
Benjamin-Ono Equation
Wave Interaction
Zero
Dispersion Relation
Korteweg-de Vries Equation
One Dimension
Wave equation
Two Dimensions
Nonlinearity
Requirements
wave interaction
planetary waves
wave equations
nonlinearity
requirements
matrices

Keywords

  • Benjamin-Ono equation
  • integrability
  • intermediate long-wave equation
  • Korteweg-de Vries equation
  • scattering matrix

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

Five-wave classical scattering matrix and integrable equations. / Zakharov, Vladimir E; Odesskii, A. V.; Cisternino, M.; Onorato, M.

In: Theoretical and Mathematical Physics, Vol. 180, No. 1, 2014, p. 759-764.

Research output: Contribution to journalArticle

Zakharov, Vladimir E ; Odesskii, A. V. ; Cisternino, M. ; Onorato, M. / Five-wave classical scattering matrix and integrable equations. In: Theoretical and Mathematical Physics. 2014 ; Vol. 180, No. 1. pp. 759-764.
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