Five-wave classical scattering matrix and integrable equations
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.
- Publication:
-
Theoretical and Mathematical Physics
- Pub Date:
- July 2014
- DOI:
- 10.1007/s11232-014-0177-7
- Bibcode:
- 2014TMP...180..759Z
- Keywords:
-
- integrability;
- intermediate long-wave equation;
- Korteweg-de Vries equation;
- Benjamin-Ono equation;
- scattering matrix