Several interaction solutions for a (3+1) dimensional Boiti-Leon-Manna-Pempinelli type equations

Abstract The main research objective of this paper is to construct several interaction solutions for a (3+1) dimensional Boiti-Leon-Manna-Pempinelli type equation, and the elastic and inelastic collisions between lump waves and kink waves are discussed. Based on the generalized bilinear operators, the new discovery is that the three sets of interaction solutions of the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli type equations are obtained by introducing several test functions. When different parameter values are selected, the one-lump-two-kink solution can explain two types of elastic collision between one lump wave and two kink waves. For some nonlinear equations that cannot be solved by the long wave limit method, the test function method is a feasible approach for discussing the elastic collision between lump waves and solitary waves. In addition, other interaction solutions can describe the excitation of a rogue wave in a pair of kink waves on a periodic background, as well as the fusion and fission of one lump wave and one kink wave on a periodic background, respectively. Specifically, when certain special parameter values are selected, the periodic background generated by periodic waves can be reduced to a plane. Previous research has focused on the interaction between lump and solitary waves on a plane. Through comparison, it can be found that the results of this study have a wider range of applications. This paper provides a good approach to constructing interaction solutions for nonlinear evolution equations, and the research conclusions can serve as theoretical references for incompressible fluids.