Soliton molecules and some novel interaction solutions to the (2+1)-dimensional B-type Kadomtsev–Petviashvili equation

Abstract

Soliton molecules may exists in both experimental and theotetical aspects. In this work, we investigate the (2+1)-dimensional B-type Kadomtsev–Petviashvili equation, which can be used to describe weakly dispersive waves propagating in the quasi media and fluid mechanics. Soliton molecules are generated by N-soliton solution and a new velocity resonance condition. Furthermore, soliton molecules can become to asymmetric solitons when the distance between two solitons of the molecule is small enough. Based on the N-soliton solution, we obtain some novel interaction solutions which component of soliton molecules, breather waves and lump waves by deal with part of parameters by applying velocity resonance, module resonance and long wave limit method, and the interactions are elastic. Finally, some graphic analysis are discussed to understand the propagation phenomena of these solutions.