JETP Letters

, 93:701 | Cite as

Compact equation for gravity waves on deep water

  • A. I. Dyachenko
  • V. E. Zakharov
Plasma, Hydro- and Gas Dynamics


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.


JETP Letter Water Wave Diagonal Part Zakharov Equation Ideal Incompressible Fluid 
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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Novosibirsk State UniversityNovosibirskRussia
  2. 2.Landau Institute for Theoretical PhysicsChernogolovka, Moscow regionRussia
  3. 3.Department of MathematicsUniversity of ArizonaTucsonUSA
  4. 4.Lebedev Physical InstituteRussian Academy of SciencesMoscowRussia

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