Evolution dynamics of fundamental mechanisms of wave propagation in gas bubble-liquid interactions and soliton solutions

Abstract This paper investigates the dynamics of solitary wave solutions based on the (3+1)-dimensional nonlinear wave equation with variable coefficients expressed to describe gas-bubble-liquid interactions. The generalised (1/G’)-expansion method, new solitary wave solutions for this equation have been successfully derived to better understand the underlying dynamics of wave phenomena, especially in gas-bubble-liquid systems. Thanks to this method, the results of the variations of physical parameters in the generated solutions are also emphasised. The physical dynamics of each dimension in the generated solutions allow both the dimensions to be compared with each other and the equation to be compared with the existing literature with a holistic understanding. With this application, we have also analyzed the direct effects of the viscosity of the fluid on the dispersion of the bubble. These solitary solutions have helped us to better explain the wave behavior in gas-bubble-liquid systems and provided a new perspective on the solution of nonlinear wave equations. The structure of the study contributes to a deeper understanding of wave phenomena by discussing the (3+1) dimensional variable coefficient nonlinear wave equation within the framework of both mathematical analysis and physical analysis.