Dynamical analysis of lump, lump-triangular periodic, predictable rogue and breather wave solutions to the (3 + 1)-dimensional gKP–Boussinesq equation

Abstract

This paper studies the dynamics of shallow water waves with the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili–Boussinesq (gKP–Boussinesq) equation arising in fluid mechanics. By the virtue of the Hirota bilinear method, a series of lump, single stripe, lump-triangular periodic, predictable rogue, and breather wave solutions are constructed to the (3 + 1)-D gKP–Boussinesq equation. For generating the breather wave solutions, two homoclinic test approaches are executed to the mentioned equation. It is seen that the breather wave propagates periodically in a certain direction with a constant period. Furthermore, for lump solutions, the shapes and amplitudes of the lump wave are found to be unchanged during its propagation. Besides, the lump-stripe soliton solutions illustrate the fission and fusion behaviors that one-stripe wave splits into one lump and one-stripe waves, and one lump and one-stripe waves merge into one-stripe wave, respectively. To interpret the underlying propagation characteristics, some attained solutions are displayed by making their 3D, density, and contour plots. All the graphs are presented to show their proper wave profiles via the obtained solutions to the studied equation. Moreover, it may be concluded that the attained solutions and their physical features might be helpful to comprehend the localized wave propagation in shallow water waves.