Fission and fusion interaction phenomena of mixed lump kink solutions for a generalized (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

Abstract

In this paper, a generalized (3[Formula: see text]+[Formula: see text]1)-dimensional B-type Kadomtsev–Petviashvili (gBKP) equation is investigated by using the Hirota’s bilinear method. With the aid of symbolic computation, some new lump, mixed lump kink and periodic lump solutions are derived. Based on the derived solutions, some novel interaction phenomena like the fission and fusion interactions between one lump soliton and one kink soliton, the fission and fusion interactions between one lump soliton and a pair of kink solitons and the interactions between two periodic lump solitons are discussed graphically. Results might be helpful for understanding the propagation of the shallow water wave.