Solitons, Breathers and Lumps for a Generalized (3 + 1)—Dimensional Kadomtsev–Petviashvili-Benjamin-Bona-Mahony Equation in a Fluid

Fluids are studied in such disciplines as atmospheric science, oceanography and astrophysics. In this paper, we investigate a generalized (3 + 1)—dimensional Kadomtsev–Petviashvili-Benjamin-Bona-Mahony equation in a fluid. Via the Hirota method, bilinear forms, soliton, breather and lump solutions of that equation are obtained. At the same time, solitons, breathers and lumps are depicted. We find that the amplitude and shape of the one soliton keep unchanged during the propagation and the interaction between the two solitons is elastic. We observe that the shapes and amplitudes of the breather and lump remain unchanged during the propagation. We present the one solitons, two solitons, breathers and lumps with the influence of the coefficients in the equation.