Solitons interactions of a triad and a quadruplet of the Kadomtsev-Petviashvili equation

Abstract

The two-dimensional form of the Korteweg-de Vries equation is given by the Kadomtsev-Petviashvili (KP) equation. The KP equation can be solved by Hirota bilinear method. The traditional group-theoretical approach can generates analytic solutions of soliton because the KP equation has infinitely many conservation laws. Two-soliton solutions of the KP equation yield a triad, quadruplet and a non-resonant soliton structures in soliton interactions. From these basic resonant structures, higher number of soliton interaction could be observed. This paper concentrates on one type of the four-soliton solutions of the KP equation that is the interaction of a triad and a quadruplet. The solution of the interaction and interaction patterns are shown in this paper.