Compact equation for gravity waves on deep water

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.