Lump, mixed lump-kink, breather and rogue waves for a B-type Kadomtsev-Petviashvili equation

Abstract

ABSTRACT The B-type Kadomtsev-Petviashvili (BKP) equations can describe certain nonlinear phenomena in the fluids. In this paper, a BKP equation is investigated. Lump-wave, mixed lump-kink wave, breather-wave and rogue-wave solutions are constructed via the symbolic computation and Hirota method. Kink-shaped traveling wave solutions are derived via the polynomial expansion method. According to the mixed lump-kink wave solutions, we graphically analyze the interactions between the lump wave and kink wave and observe that (1) after the fission of the kink wave, the kink wave splits into one kink wave and one lump wave; (2) after the fusion between the lump and kink waves, the lump and kink merge together. Besides, we discuss the fission-fusion phenomenon between the lump wave and a pair of the kink waves and find that the higher kink wave splits into a kink wave and a lump wave, and then the lump wave and the lower kink wave merge together. Breather waves are displayed, based on which we construct the rogue waves with the periods of the breather waves becoming the infinity.