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Teoreticheskaya i Matematicheskaya Fizika, 2014, Volume 180, Number 1, Pages 10–16
DOI: https://doi.org/10.4213/tmf8639 (Mi tmf8639) 		 
This article is cited in 5 scientific papers (total in 5 papers)

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
Full-text PDF (380 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf8639
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.
Received: 13.01.2014
English version:
Theoretical and Mathematical Physics, 2014, Volume 180, Issue 1, Pages 759–764
DOI: https://doi.org/10.1007/s11232-014-0177-7
Bibliographic databases:
Language: Russian
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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\paper Five-wave classical scattering matrix and integrable equations
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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