Bright/dark breather-soliton, lump wave-soliton and rogue wave-soliton interactions for a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation in fluid mechanics

Fluid mechanics is concerned with the mechanics of liquids, plasmas and gases, with the forces on them. Investigated in this paper is a generalized (3+1)-dimensional B-type Kadomtsev-Petviashvili equation for the weakly dispersive waves in fluid mechanics. Breather-soliton, lump wave-soliton and rogue wave-soliton solutions are derived under certain integrable constraints via the Hirota method. We display two types of the interactions between a breather and a soliton. Interactions among a breather and two solitons are shown. We observe the fusion between a dark lump wave and a dark soliton, as well as the fission of a dark soliton. Studying the rogue wave-soliton interactions, we find that a rogue wave appears from one soliton and merges into the other soliton gradually. In addition, effects of h(1), h(3) and h(5) on those waves are observed, where h(1), h(3) and h(5) are the coefficients in that equation.