Lie group theory, stability analysis with dispersion property, new soliton solutions and conserved quantities of 3D generalized nonlinear wave equation in liquid containing gas bubbles with applications in mechanics of fluids, biomedical sciences and cell biology

Abstract

Nonlinear wave equations emerge naturally in optics as well as fluid dynamics. It is noteworthy that, an essential class of special solutions that satisfy the underlying equations are observed to be localized waves, which are frequently referred to as solitons or solitary waves. Thus, in the context of small amplitude alongside shallow-water waves, such solutions were discovered in the nineteenth century. Therefore, we present in this paper, the analytical investigations accomplished on a three dimensional generalized nonlinear wave equation in a fluid accommodating gas fizzes with applications. This equation was developed in the field within which liquid in conjunction with gas fizzes exists to describe the proliferation of feebly-nonlinear-waves. The underlying equation is transformed into a nonlinear structured ordinary differential equation (NLODE) by Lie group theory. Direct integration of the resulting NLODE produced periodic, trigonometric bright soliton together with singular soliton solutions. Moreover, some general exact soliton solutions of the equation under study are secured via the simplest equation technique (SET) in the structure of various Jacobi elliptic functions. Thus, we secure diverse periodic solitons of the equation under consideration. In addition, the dynamics of the results are depicted using suitable graphs which were also discussed. Furthermore, We conduct stability analysis on the model under study and outline the significance of our results in fluid dynamics, biomedical sciences and biological cells. Conclusively, we constructed conservation laws of the aforementioned equation by invoking Ibragimov’s theorem for conserved quantities via its formal Lagrangian structure.