Dark breather waves, dark lump waves and lump wave–soliton interactions for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in a fluid. (1st July 2019) - Hu, Cong-Cong; Tian, Bo; Yin, Hui-Min; Zhang, Chen-Rong; Zhang, Ze
Abstract: Fluids are seen in a wide range of disciplines, including mechanical, civil, chemical and biomedical engineering, geophysics, astrophysics and biology. In this paper, we investigate a ( 3 + 1 ) -dimensional generalized Kadomtsev–Petviashvili equation for the long water waves and small-amplitude surface waves with the weak nonlinearity, weak dispersion and weak perturbation in a fluid. Breather-wave, lump-wave and lump wave–soliton solutions are derived under certain conditions via the Hirota method. With h 1 h 2 − 1 < 0, where h 1 and h 2 represent the coefficients of dispersion and nonlinearity, respectively, we obtain the dark breather wave and lump wave. We observe the effects of h 1, h 2, h 4, h 6 and h 8 on the dark breather wave and lump wave, where h 6 is the perturbed effect, h 4 and h 8 stand for the disturbed wave velocity effects corresponding to the y and z coordinates: h 1 and h 2 influence the amplitude of the dark breather wave; h 1, h 4 and h 8 influence the distance between the adjacent valleys of the dark breather wave; h 1, h 4, h 6 and h 8 influence the location of the dark breather wave; h 2, h 4, h 6 and h 8 influence the amplitude of the dark lump wave; h 1, h 4 and h 8 influence the width of the dark lump wave; h 4, h 6 and h 8 influence the location of the dark lump wave. When h 1 h 2 − 1 > 0, we present the fusion between a bright lump wave and one bright soliton as well as fission of one bright soliton. We also observe the fusion between a dark lump wave and one dark soliton as well as fission of one dark soliton with h 1 h 2 − 1 > 0 .