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

Abstract

In this paper, we theoretically investigate the four-soliton interaction and their resonance phenomena of the (3+1)-dimensional Kadomtsev—Petviashvili (KP) equation. We find that the maximum amplitude of the resonantly created soliton can be 16 times that of one of the four equi-amplitude initial interacting solitons. We also find that the maximum amplitude can only be 4 times the initial soliton amplitude when the resonance phenomena does not take place. The case of four solitons with different amplitudes also has been studied analytically. The results indicate that the resonance phenomena still exists in this case. Numerical results confirm the theoretical predictions.