Some interaction solutions on the periodic background in the (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Abstract

This study aims to discuss several types of inelastic collision phenomena between lump waves and kink waves on a periodic background. Based on the generalized bilinear method, a series of new interaction solutions for the (3 + 1) dimensional Boiti–Leon–Manna–Pempinelli equation are constructed by introducing several types of test functions. These interaction solutions can describe several novel nonlinear phenomena of lump wave and kink wave on a periodic wave background, including inelastic collisions of single lump wave and double kink wave, inelastic collisions of single lump wave and triple kink wave, evolution of double lump waves, fusion and fission of double lump waves and single kink wave, and inelastic collisions of double lump waves and a pair of kink waves. That is to say, the novelty of this article is that the obtained some new exact solutions can describe the interaction between lump waves, kink waves, and periodic waves. It can be seen that the test function method is an effective method for solving nonlinear evolution equations, and the research conclusions of this paper have potential application value for the study of nonlinear theory.