Periodic Wave Patterns of two-dimensional Boussinesq systems

Abstract

We prove the existence of a large family of two-dimensional travelling wave patterns for a Boussinesq system which describes three-dimensional water waves. This model equations result from full Euler equations in assuming that the depth of the fluid layer is small with respect to the horizontal wave length, and that the flow is potential, with a free surface without surface tension. Our proof uses Lyapunov-Schmidt method which may be managed here, contrary to the case of gravity waves with full Euler equations. Our results are in a good agreement with experimental results.