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VOLUME 93 | ISSUE 12 | PAGE 782
Compact equation for gravity waves on deep water
A. I. Dyachenko^{\nabla\square}, V. E. Zakharov^{\nabla\square\bigcirc*}
Novosibirsk State University, 630090 Novosibirsk, Russia
^\squareLandau Institute for Theoretical Physics, 142432 Chernogolovka, Russia
^\bigcircDepartment of Mathematics, University of Arizona, 857201 Tucson, AZ, USA
*Physical Institute of RAS, Leninskiy prospekt, 53, Moscow, 119991, Russia

Abstract
Using the fact of vanishing four waves interaction for water gravity waves for 2D potential fluid we were able significantly simplify well-known but cumbersome Zakharov equation. Hamiltonian of the obtained equation is very simple and includes only fourth order nonlinear term. It rises the question about integrability of the free surface hydrodynamics. This new equation is very suitable as for analytic study as for numerical simulation.


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