Interaction of edge waves with swell on a beach

Excitation of edge waves on a beach by incoming swell is considered on the basis of shallow-water model. Subharmonic resonance mechanism of interaction is analyzed by multi-scaled expansion asymptotic techniques. The generation of edge waves between wave breakers is found to have a dynamic threshold. It is defined by intensity and frequency of incoming swell, geometry of a shore zone. Nonlinear no stationary wave solutions for the envelope of interacting edge waves are described by generalized Sine-Gordon model. An infinite set of exact solutions are received by the Lamb method for the phase synchronism regime of wave's interaction.