Elastic and inelastic collisions in the (2 + 1)-dimensional modified dispersive water wave equation

The research objective of this paper is to improve the exp [-ϕ(ξ)] expansion method and discuss elastic and inelastic collisions (the fusion and fission) of multiple localized waves. Based on variable separation transformation, a series of new variable separation solutions for the (2 + 1)-dimensional modified dispersive water wave equation are constructed using the improved exp[-ϕ(ξ)]] expansion method. By introducing some appropriate functions, the three-dimensional images of variable separation solutions are provided to investigate the structural characteristics and dynamic behavior of these solutions. The variable separation solutions exhibit two inelastic collisions phenomena: multiple dromion waves fuse into one dromion wave, and one periodic dromion wave splits into multiple periodic dromion waves. In addition, the “head-on” elastic collision, “chasing” elastic collision, and “head on-chasing” elastic collision of multiple periodic dromion waves are discussed, as well as the inelastic collision of two dromion solitons in a plane (on a periodic background). It is hoped that the interaction phenomenon of nonlinear waves discussed in this paper can provide a certain positive effect on the study of soliton theory.