Dark breather waves, dark lump waves and lump wave-soliton interactions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in a fluid

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 they 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. (C) 2019 Elsevier Ltd. All rights reserved.