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

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Pis'ma v Zhurnal Èksperimental'noi i Teoreticheskoi Fiziki, 2013, Volume 98, Issue 1, Pages 48–52
DOI: https://doi.org/10.7868/S0370274X13130109 (Mi jetpl3463)

This article is cited in 20 scientific papers (total in 20 papers)

NONLINEAR DYNAMICS

On the nonintegrability of the free surface hydrodynamics

A. I. Dyachenko^ab, D. I. Kachulin^b, V. E. Zakharov^abcd

^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

Full-text PDF (231 kB) Citations (20)

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

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.

Received: 21.05.2013

English version:
Journal of Experimental and Theoretical Physics Letters, 2013, Volume 98, Issue 1, Pages 43–47
DOI: https://doi.org/10.1134/S002136401314004X

Bibliographic databases:

Document Type: Article

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

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https://www.mathnet.ru/eng/jetpl3463

https://www.mathnet.ru/eng/jetpl/v98/i1/p48

This publication is cited in the following 20 articles:

Guobin Lin, Hu Huang, Symmetry, 16:5 (2024), 618
Fang He, Yifan Zhang, Haonan Jiang, Can Huang, Physics of Fluids, 35:2 (2023)
Kachulin D., Dremov S., Dyachenko A., Fluids, 6:3 (2021), 115
Kachulin D., Dyachenko A., Dremov S., Fluids, 5:2 (2020), 65
Dyachenko I A., Lushnikov P.M., Zakharov V.E., J. Fluid Mech., 869 (2019), PII S0022112019002192, 526–552
Dyachenko I A., Dyachenko S.A., Lushnikov P.M., Zakharov V.E., J. Fluid Mech., 874 (2019), PII S0022112019004488, 891–925
Kachulin D., Dyachenko A., Gelash A., Fluids, 4:2 (2019), 83
D.I. Kachulin, A.A. Gelash, A.I. Dyachenko, V.E. Zakharov, JOR, 47:1 (2019), 66
D. Kachulin, A. Gelash, Nonlinear Process Geophys., 25:3 (2018), 553–563
G. Khakimzyanov, D. Dutykh, Commun. Comput. Phys., 23:5 (2018), 1289–1354
A. I. Dyachenko, D. I. Kachulin, V. E. Zakharov, J. Fluid Mech., 828 (2017), 661–679
A. I. Dyachenko, D. I. Kachulin, V. E. Zakharov, J. Ocean Eng. Mar. Energy, 3:4 (2017), 409
Dyachenko A.I., Kachulin D.I., Zakharov V.E., Stud. Appl. Math., 137:2 (2016), 189–198
Dyachenko A.I., Kachulin D.I., Zakharov V.E., Nat. Hazards, 84:2 (2016), S529–S540
A. I. Dyachenko, D. I. Kachulin, V. E. Zakharov, Extreme Ocean Waves, 2016, 23
JETP Letters, 102:8 (2015), 513–517
Onorato M., Vozella L., Proment D., Lvov Yu.V., Proc. Natl. Acad. Sci. U. S. A., 112:14 (2015), 4208–4213
V. E. Zakharov, A. V. Odesskii, M. Cisternino, M. Onorato, Theoret. and Math. Phys., 180:1 (2014), 759–764
Fedele F., J. Fluid Mech., 748 (2014), 692–711
A I Dyachenko, D I Kachulin, V E Zakharov, J. Phys.: Conf. Ser., 510 (2014), 012050

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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