Abundant soliton wave solutions and the linear superposition principle for generalized (3+1)-D nonlinear wave equation in liquid with gas bubbles by bilinear analysis

In this article, we study the generalized (3+1)-dimensional nonlinear wave equation where is investigated in soliton theory and by employing the Hirota's bilinear method the bilinear form is obtained, and the N-soliton solutions are constructed. In addition, some Lump solutions, Lump-kink solutions, Lump-two kink solutions, Lump-periodic solutions, its Interaction solutions, Cross-kink wave, Breather-type, Multi wave, Periodic wave solutions, and Solitary wave solutions of the addressed equation with specific coefficients are shown. Finally, under certain conditions the asymptotic behavior of the two-soliton solution is analyzed to prove that the collision of the two-soliton is elastic. Moreover, we employ the linear superposition principle to determine N-soliton wave solutions for the generalized (3+1)-dimensional nonlinear wave equation in liquid with gas bubbles.