Lumps with their some interactions and breathers to an integrable (2 + 1)-dimensional Boussinesq equation in shallow water

Abstract

In this paper, the lumps with their interactions (lump-single and lump-double stripes), and breather wave solutions are constructed to the new integrable (2 + 1)-dimensional Boussinesq equation via the Hirota bilinear method. The propagations of the obtained lumps, lump-stripes, and breather wave solutions of the aforesaid equation are presented through some 3D and 2D graphs. All of the graphs are given to show their correct wave profiles. The graphical outputs demonstrate that lump waves propagate in all directions throughout space. However, the amplitudes and forms of lump waves remain constant during their propagation in any direction. On the other hand, the lump wave travels along with the stripes for the lump and stripes solutions. Furthermore, two homoclinic test approaches are used to produce the breather wave solutions to the aforesaid equation. It is found that breather waves propagate in a specific direction on a constant period. In addition, the effects of constant coefficients of the model are presented also graphically. It is found that the amplitudes of all obtained wave solutions are changed with the change of constant coefficients of the model..The outcomes of the study can be useful for a better understanding of wave propagation dynamics in shallow water under gravity.