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TMF, 2014, Volume 180, Number 1, Pages 10–16 (Mi tmf8639)  

Five-wave classical scattering matrix and integrable equations

V. E. Zakharovabc, A. V. Odesskiid, M. Cisterninoe, M. Onoratofe

a Lebedev Physical Institute, RAS, Moscow, Russia
b University of Arizona, Tucson, USA
c Novosibirsk State University, Novosibirsk, Russia
d Brock University, St. Catharines, Canada
e Dipartimento di Fisica, Università di Torino, Torino, Italy
f INFN, Sezione di Torino, Torino, Italy

Abstract: We study the five-wave classical scattering matrix for nonlinear and dispersive Hamiltonian equations with a nonlinearity of the type $u  \partial u/\partial x$. Our aim is to find the most general nontrivial form of the dispersion relation $\omega(k)$ 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.

Keywords: integrability, intermediate long-wave equation, Korteweg–de Vries equation, Benjamin–Ono equation, scattering matrix

DOI: https://doi.org/10.4213/tmf8639

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English version:
Theoretical and Mathematical Physics, 2014, 180:1, 759–764

Bibliographic databases:

Received: 13.01.2014

Citation: V. E. Zakharov, A. V. Odesskii, M. Cisternino, M. Onorato, “Five-wave classical scattering matrix and integrable equations”, TMF, 180:1 (2014), 10–16; Theoret. and Math. Phys., 180:1 (2014), 759–764

Citation in format AMSBIB
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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