Soliton and Lump Solutions of a (3+1)-dimensional Generalized B-type Kadomtsev-Petviashvili Equation in Fluid Mechanics

Abstract

In this paper, we investigate the soliton and lump solutions of a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation in fluid mechanics. Through logarithmic transformation, we derive its bilinear form. Via the bilinear equation, both first-order and second-order soliton solutions of this eqaution are constructed. Furthermore, semi-rational solutions of this equation are obtained via Gram determinant approach. Specifically, lump chains and lump-kink solutions of this equation are successfully derived. The analytical results reveal that solitary waves propagate at constant velocities with their amplitudes and velocities exhibiting a proportional relationship. This implies that adjustments to the parameters will concurrently affect both the propagation velocity and amplitude of solitary waves. By employing contour figures and auxiliary lines, the periods and propagation velocities of lump chains and lump-kink waves are systematically computed. Notably, as the parameter N (the order of these solutions) increases, phenomena of fusion or fission emerge among these nonlinear waves. Additionally, by adjusting parameter, distinct types of lump waves can be observed that propagate along with the coordinate axes.