Abstract
In this paper we propose two Hamiltonian models to describe two-dimensional deep water waves propagating on the surface of an ideal incompressible three-dimensional fluid. The idea is based on taking advantage of the Zakharov equation for one-dimensional waves which can be written in the form of so-called compact equations. We generalize these equations to the case of two-dimensional waves. As a test of our models, we perform numerical simulations of the dynamics of standing waves in a channel with smooth vertical walls. The results obtained in the proposed models are comparable, indicating that the models are similar to the original Zakharov equation.
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