Rogue waves and lump solutions for a (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation in fluid mechanics

Abstract

Under investigation in this letter is a (3[Formula: see text]+[Formula: see text]1)-dimensional generalized B-type Kadomtsev-Petviashvili equation, which describes the weakly dispersive waves propagating in a fluid. Employing the Hirota method and symbolic computation, we obtain the lump, breather-wave and rogue-wave solutions under certain constraints. We graphically study the lump waves with the influence of the parameters [Formula: see text], [Formula: see text] and [Formula: see text] which are all the real constants: When [Formula: see text] increases, amplitude of the lump wave increases, and location of the peak moves; when [Formula: see text] increases, lump wave’s amplitude decreases, but location of the peak keeps unchanged; when [Formula: see text] changes, lump wave’s peak location moves, but amplitude keeps unchanged. Breather waves and rogue waves are displayed: Rogue waves emerge when the periods of the breather waves go to the infinity.