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Pis'ma v Zh. Èksper. Teoret. Fiz., 2013, Volume 98, Issue 1, Pages 48–52 (Mi jetpl3463)  

This article is cited in 10 scientific papers (total in 10 papers)

NONLINEAR DYNAMICS

On the nonintegrability of the free surface hydrodynamics

A. I. Dyachenkoab, D. I. Kachulinb, V. E. Zakharovabcd

a Novosibirsk State University
b Landau Institute for Theoretical Physics, Russian Academy of Sciences
c University of Arizona, Department of Mathematics
d P. N. Lebedev Physical Institute, Russian Academy of Sciences

Abstract: We study integrability of the compact 1-D Zakharov equation. The results of numerical experiments on multiple collisions of breathers (which correspond to envelope solitons in the NLSE approximation) show that collisions are not pure elastic. Also we analyse the amplitude of six-wave interactions for compact 1-D Zakharov equation. It was found that six-wave amplitude is not canceled for this equation. Thus, 1-D Zakharov equation is not integrable.

DOI: https://doi.org/10.7868/S0370274X13130109

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English version:
Journal of Experimental and Theoretical Physics Letters, 2013, 98:1, 43–47

Bibliographic databases:

Document Type: Article
Received: 21.05.2013
Language: English

Citation: A. I. Dyachenko, D. I. Kachulin, V. E. Zakharov, “On the nonintegrability of the free surface hydrodynamics”, Pis'ma v Zh. Èksper. Teoret. Fiz., 98:1 (2013), 48–52; JETP Letters, 98:1 (2013), 43–47

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. E. Zakharov, A. V. Odesskii, M. Cisternino, M. Onorato, “Five-wave classical scattering matrix and integrable equations”, Theoret. and Math. Phys., 180:1 (2014), 759–764  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. Fedele F., “On Certain Properties of the Compact Zakharov Equation”, J. Fluid Mech., 748 (2014), 692–711  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. JETP Letters, 102:8 (2015), 513–517  mathnet  crossref  crossref  isi  elib
    4. Onorato M., Vozella L., Proment D., Lvov Yu.V., “Route To Thermalization in the Alpha-Fermi-Pasta-Ulam System”, Proc. Natl. Acad. Sci. U. S. A., 112:14 (2015), 4208–4213  crossref  adsnasa  isi  scopus
    5. Dyachenko A.I., Kachulin D.I., Zakharov V.E., “Probability Distribution Functions of Freak Waves: Nonlinear Versus Linear Model”, Stud. Appl. Math., 137:2 (2016), 189–198  crossref  mathscinet  zmath  isi  elib  scopus
    6. Dyachenko A.I., Kachulin D.I., Zakharov V.E., “About compact equations for water waves”, Nat. Hazards, 84:2 (2016), S529–S540  crossref  mathscinet  isi  scopus
    7. A. I. Dyachenko, D. I. Kachulin, V. E. Zakharov, “Super Compact Equation For Water Waves”, J. Fluid Mech., 828 (2017), 661–679  crossref  mathscinet  isi  scopus
    8. D. Kachulin, A. Gelash, “On the phase dependence of the soliton collisions in the dyachenko-zakharov envelope equation”, Nonlinear Process Geophys., 25:3 (2018), 553–563  crossref  isi  scopus
    9. G. Khakimzyanov, D. Dutykh, “Numerical modelling of surface water wave interaction with a moving wall”, Commun. Comput. Phys., 23:5 (2018), 1289–1354  crossref  mathscinet  isi
    10. Dyachenko I A., Lushnikov P.M., Zakharov V.E., “Non-Canonical Hamiltonian Structure and Poisson Bracket For Two-Dimensional Hydrodynamics With Free Surface”, J. Fluid Mech., 869 (2019), PII S0022112019002192, 526–552  crossref  isi  scopus
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