Abundant soliton wave solutions for the (3+1)-dimensional variable-coefficient nonlinear wave equation in liquid with gas bubbles by bilinear analysis

In this paper, we check and scan the (3+1)-dimensional variable-coefficient nonlinear wave equation which is considered in soliton theory and generated by considering the Hirota bilinear operators. We retrieve some novel exact analytical solutions, including cross-kink soliton solutions, breather wave solutions, interaction between stripe and periodic, multi-wave solutions, periodic wave solutions and solitary wave solutions for the (3+1)-dimensional variable-coefficient nonlinear wave equation in liquid with gas bubbles by Maple symbolic computations. The required conditions of the analyticity and positivity of the solutions can be easily achieved by taking special choices of the involved parameters. The main ingredients for this scheme are to recover the Hirota bilinear forms and their generalized equivalences. Lastly, the graphical simulations of the exact solutions are depicted.

Automated summary

This paper verifies and scans the (3+1)-dimensional variable-coefficient nonlinear wave equation, which is generated by considering the Hirota bilinear operators and considering soliton theory. By using Maple symbolic computations, some novel exact analytical solutions are obtained, including cross-kink soliton solutions, breather wave solutions, interaction between stripe and periodic waves, multi-wave solutions, periodic wave solutions, and solitary wave solutions. The analyticity and positivity of the solutions can be easily achieved by selecting specific parameters. The main contribution of this work is the recovery of the Hirota bilinear forms and their generalized equivalences. Graphical simulations of the exact solutions are also presented.