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Compact equation for gravity waves on deep water |
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| Authors: | A. I. Dyachenko,V. E. Zakharov |
| Affiliation: | 1.Novosibirsk State University,Novosibirsk,Russia;2.Landau Institute for Theoretical Physics,Chernogolovka, Moscow region,Russia;3.Department of Mathematics,University of Arizona,Tucson,USA;4.Lebedev Physical Institute,Russian Academy of Sciences,Moscow,Russia |
| 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. |
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