Compact equation for gravity waves on deep water

A. I. Dyachenko; V. E. Zakharov

doi:10.1134/S0021364011120058

Compact equation for gravity waves on deep water

A. I. Dyachenko
, V. E. Zakharov

Research output: Contribution to journal › Article › peer-review

38 Scopus citations

Abstract

Using the fact of vanishing four waves interaction for water gravity waves for 2D potential fluid, we have significantly simplified the well-known but cumbersome Zakharov equation. The Hamiltonian of the obtained equation is very simple and includes only the fourth order nonlinear term. It raises the question of the integrability of free surface hydrodynamics. This new equation is very suitable both for analytic study and for numerical simulation.

Original language	English (US)
Pages (from-to)	701-705
Number of pages	5
Journal	JETP Letters
Volume	93
Issue number	12
DOIs	https://doi.org/10.1134/S0021364011120058
State	Published - Aug 2011
Externally published	Yes

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

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Cite this

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title = "Compact equation for gravity waves on deep water",

abstract = "Using the fact of vanishing four waves interaction for water gravity waves for 2D potential fluid, we have significantly simplified the well-known but cumbersome Zakharov equation. The Hamiltonian of the obtained equation is very simple and includes only the fourth order nonlinear term. It raises the question of the integrability of free surface hydrodynamics. This new equation is very suitable both for analytic study and for numerical simulation.",

author = "Dyachenko, \{A. I.\} and Zakharov, \{V. E.\}",

note = "Funding Information: This work was supported by the Government of Russian Federation (project no. 11.G34.31.0035 for support of scientific research leading by V.E. Zakharov at the Novosibirsk State University), by the US Office of Naval Research (grant no. 00014 06 C 0130), by the US National Science Foundation (grant no. DMS 0404577), by the National Oceanographic Partnership Program (grant “Two Scale Approximation for Wind Generated Ocean Surface Waves”), by the Russian Foundation for Basic Research (project nos. 09 01 00631 and 09 05 13605), by the Presidium of the Rus sian Academy of Sciences (program “Fundamental Problems in Nonlinear Dynamics”), and by the Council of the President of the Russian Federation for Support of Young Scientists and Leading Scientific Schools.",

year = "2011",

month = aug,

doi = "10.1134/S0021364011120058",

language = "English (US)",

volume = "93",

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AU - Zakharov, V. E.

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PY - 2011/8

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N2 - Using the fact of vanishing four waves interaction for water gravity waves for 2D potential fluid, we have significantly simplified the well-known but cumbersome Zakharov equation. The Hamiltonian of the obtained equation is very simple and includes only the fourth order nonlinear term. It raises the question of the integrability of free surface hydrodynamics. This new equation is very suitable both for analytic study and for numerical simulation.

AB - Using the fact of vanishing four waves interaction for water gravity waves for 2D potential fluid, we have significantly simplified the well-known but cumbersome Zakharov equation. The Hamiltonian of the obtained equation is very simple and includes only the fourth order nonlinear term. It raises the question of the integrability of free surface hydrodynamics. This new equation is very suitable both for analytic study and for numerical simulation.

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Compact equation for gravity waves on deep water

Abstract

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