Nonlinear dynamics of soliton molecules, hybrid interactions and other wave solutions for the (3+1)-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation

Abstract

This work plumbs the nonlinear dynamics of the ([Formula: see text])-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation (gKPBe), which is used to describe some interesting physical phenomena in the fields of fluids. The resonance conditions of the soliton molecules on the ([Formula: see text]), ([Formula: see text]) and ([Formula: see text]) planes are investigated and the soliton molecules are obtained on the basis of the N-soliton solutions that are extracted by virtue of the Hirota form. Furthermore, some novel hybrid interactions including the interaction between the soliton and soliton molecule, the interaction between the different soliton molecules are also explored. Finally, the sub-equation approach is exerted to explore the various wave solutions, which include the kinky wave, bright-dark wave and the singular periodic wave solutions. Correspondingly, the graphical descriptions of the attained solutions are drawn to present a better understanding of the physical attributes. The derived solutions can enlarge the exact solutions of the ([Formula: see text])-dimensional gKPBe and lead us to understand the nonlinear dynamic behaviors better.