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.

Investigation on the resonance phenomena of multi-solitons for the (3+1)-dimensional Kadomtsev—Petviashvili equation

“…[5] Subsequently, we investigated the res-onance phenomena of three equi-amplitude solitons of the (2+1)-dimensional KP equation. [6] It was found theoretically and confirmed numerically that the maximum amplitude will be 9 times that of one of the initial interacting solitons. This resonance amplitude enhancement has been observed in experiments performed in fluid dynamics, [3,4] and also in the plasma physics.…”

“…In Ref. [6], we find that when the resonance takes place among three solitons with the same amplitudes, the maximum amplitude is 9 times that of the initial interacting solitons. In this paper, we find that when resonance takes place among four solitons with the same amplitudes, the maximum amplitude of the newly created soliton can be 16 times that of the initial interacting soliton.…”