Novel interaction phenomena of localized waves in the generalized (3+1)-dimensional KP equation

Abstract

Based on Hirota bilinear method, the N-soliton solution of the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation is derived explicitly, from which some localized waves such as soliton, breather, lump and their interactions are obtained by the approach of long wave limit. Especially, by selecting particular parameter constraints in the N-soliton solutions, the one breather or one lump can be obtained from two-soliton; the elastic interaction solutions between one bell-shaped soliton and one breather or between one bell-shaped soliton and one lump can be obtained from three-soliton; the elastic interaction solutions among two bell-shaped solitons and one breather, among two bell-shaped solitons and one lump, between two breathers or between two lumps can be obtained from four-soliton; the elastic interactions solutions among one bell-shaped soliton and two breathers, among one breather and three bell-shaped solitons, among one lump and three bell-shaped solitons, among one bell-shaped soliton and two breathers or among one breather, one lump and one bell-shaped soliton can be obtained from five-soliton. Detailed behaviors of such interaction phenomena are illustrated analytically and graphically. The results obtained in this paper may be helpful for understanding the evolution of nonlinear localized waves in shallow water.