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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∂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.
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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    • This publication is cited in the following 5 articles:
    1. Zitong Chen, Man Jia, Ruoxia Yao, S.Y. Lou, “Symmetry study of a novel integrable supersymmetric dispersionless system”, Applied Mathematics Letters, 154 (2024), 109080  crossref
    2. B. Gormley, E.V. Ferapontov, V.S. Novikov, M.V. Pavlov, “Integrable systems of the intermediate long wave type in 2+1 dimensions”, Physica D: Nonlinear Phenomena, 435 (2022), 133310  crossref
    3. Jin K., Ma X., “Cancellations of Resonances and Long Time Dynamics of Cubic Schrodinger Equation on T”, Commun. Math. Phys., 381:3 (2021), 1309–1368  crossref  mathscinet  isi  scopus
    4. Redor I., Michallet H., Mordant N., Barthelemy E., “Experimental Study of Integrable Turbulence in Shallow Water”, Phys. Rev. Fluids, 6:12 (2021), 124801  crossref  mathscinet  isi
    5. Lou S.Y., Hu X.B., Liu Q.P., “Duality of Positive and Negative Integrable Hierarchies Via Relativistically Invariant Fields”, J. High Energy Phys., 2021, no. 7, 58  crossref  mathscinet  isi
    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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