Lump waves and breather waves for a (3+1)-dimensional generalized Kadomtsev–Petviashvili Benjamin–Bona–Mahony equation for an offshore structure

Abstract

In this paper, we investigate a (3[Formula: see text]+[Formula: see text]1)-dimensional generalized Kadomtsev–Petviashvili Benjamin–Bona–Mahony equation, which describes the fluid flow in the case of an offshore structure. By virtue of the Hirota method and symbolic computation, bilinear forms, the lump-wave and breather-wave solutions are derived. Propagation characteristics and interaction of lump waves and breather waves are graphically discussed. Amplitudes and locations of the lump waves, amplitudes and periods of the breather waves all vary with the wavelengths in the three spatial directions, ratio of the wave amplitude to the depth of water, or product of the depth of water and the relative wavelength along the main direction of propagation. Of the interactions between the lump waves and solitons, there exist two different cases: (i) the energy is transferred from the lump wave to the soliton; (ii) the energy is transferred from the soliton to the lump wave.