Solitons to rogue waves transition, lump solutions and interaction solutions for the (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation in fluid dynamics

摘要

In this work, we investigate the (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili (gBKP) equation in fluid dynamics, which plays an important role in depicting weakly dispersive waves propagated in a quasi-media and fluid mechanics. By employing Hirota's bilinear method, we derive the one- and two-soliton solutions of the equation. Moreover, we reduce those soliton solutions to the periodic line waves and exact breather waves by considering different parameters. A long wave limit is used to derive the rogue wave solutions. Based on the resulting bilinear representation, we introduce two types of special polynomial functions, which are employed to find the lump solutions and interaction solutions between lump and stripe soliton. It is hoped that our results can be used to enrich dynamic behaviours of the (3+1)-dimensional BKP-type equations.