Five-wave classical scattering matrix and integrable equations

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

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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
Issue number1
StatePublished - Aug 2014


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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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