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
Guiping Shen, Jalil Manafian, Dinh Tran Ngoc Huy, Kottakkaran Sooppy Nisar, Mostafa Abotaleb, Nguyễn Đình Trung
Abstract
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.