Interaction and resonance phenomena of multi-soliton

Abstract

As is well known, Korteweg-de Vries equation is a typical one which has planar solitary wave. By considering higher order transverse disturbance to planar solitary waves, we study a Kadomtsev-Petviashvili (KP) equation and find some interesting results. In this letter we investigate the three soliton interaction and their resonance phenomena of KP equation, and theoretically find that the maximum amplitude is 9 times of the initial interacting soliton for three same amplitude solitons. Three arbitrary amplitude soliton interaction of KP equation is also studied by numerical simulation, which can also results in resonance phenomena.