Multiple solitary wave interactions

Abstract

Theoretical solutions of two-soliton resonance show the possibility that the amplitude of soliton resonance is four times as large as the incident solitary wave at the critical angle. The two-soliton interaction with a symmetrical configuration is generally categorized into (3142)-type and (2143)-type (O-type). Previous studies demonstrated that amplification factors of (3142)-type and O-type are successfully reproduced by using a function of the modified Miles' prediction, κ, in which (3142)-type and O-type correspond to 0<κ<1 and κ>1. However, a train of solitary waves often occurs in shallow water, resulting in multiple solitary wave interactions. Therefore, it is necessary to investigate the interaction of multiple solitary waves due to soliton resonance. We, thus, applied theoretical solutions to analyze the interaction of multiple solitary waves, which was validated by using numerical simulations based on the variational principle. It was revealed that the second and the subsequent soliton resonances are O-type when κ is larger than zero.