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 language | English (US) |
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Pages (from-to) | 759-764 |
Number of pages | 6 |
Journal | Theoretical and Mathematical Physics |
Volume | 180 |
Issue number | 1 |
DOIs | |
State | Published - Aug 2014 |
Keywords
- Benjamin-Ono equation
- Korteweg-de Vries equation
- integrability
- intermediate long-wave equation
- scattering matrix
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics