In this work, a new extended shallow water wave equation in (3+1) dimensions is studied, which represents abundant physical meaning in nonlinear shallow water wave. We discuss the interaction between lump wave and single solitary wave, which is an inelastic collision. Further, the interaction between lump wave and two solitary waves, and the interaction between lump wave and periodic wave are also studied. Finally, the interaction among lump, periodic and one solitary waves is investigated. The dynamic properties of the obtained results are shown and analyzed by some three-dimensional images.

This paper aims to construct new mixed-type periodic and lump-type solutions via the dependent variable transformation and the Hirota’s bilinear form (general bilinear techniques). This study will be investigated by considering the (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation which describes the weakly dispersive waves in a homogenous medium in fluid dynamics. The obtained solutions contain abundant physical structure. Consequently, the dynamical behaviors of these solutions are graphically discussed for different choices of the free parameters through 3D- and contour plots.