Lump wave-soliton and rogue wave-soliton interactions for a (3+1)-dimensional B-type Kadomtsev-Petviashvili equation in a fluid

Studied in this paper is a (3 + 1)-dimensional B-type Kadomtsev-Petviashvili equation, which describes the weakly dispersive waves propagating in a fluid. Lump wave-soliton and rogue wave-soliton solutions are derived. Studying the lump wave-soliton interactions, we investigate five different phenomena between a lump wave and one soliton: Fusion phenomena during the interaction between the same/opposite directional lump wave and one soliton; Fission phenomena during the interaction between the same/opposite directional lump wave and one soliton; A lump wave traveling together with one soliton. Through the rogue wave-soliton interactions, we observe that a rogue wave appears from one soliton and merges into the other soliton gradually. Amplitude of the rogue wave reaches the maximum at a certain time, which is almost nine times of the amplitude of the soliton.