Resonantly interacting solitary waves

Abstract

Resonant (phase-locked) interactions among three obliquely oriented solitary waves are studied. It is shown that such interactions are associated with the parametric end points of the singular regime for interactions between two solitary waves. The latter include regular reflexion at a rigid wall, which is impossible for )½ ( = amplitude/depth [double less-than sign] 1), and it is shown that the observed phenomenon of can be described as a resonant interaction in this regime. The run-up at the wall is calculated as a function of )½ and is found to have a maximum value of 4i = (3 i, )½, and suggests that a solitary wave cannot turn through an angle in excess of (3α)½ at a convex corner without separating or otherwise losing its identity.