New exact solitary wave solutions of the generalized (3 + 1)-dimensional nonlinear wave equation in liquid with gas bubbles via extended auxiliary equation method

This article will investigate the exact solitary wave solutions of the (3 + 1) generalized nonlinear wave equation with gas bubbles. Gas bubble-containing liquids are frequently seen in physics, engineering, science, and other fields. We explored this model using the extended auxiliary equation method. This method gives many essential solitary wave solutions, ranging from exponential to trigonometric and hyperbolic wave solutions. The investigated solutions are entirely different and new to the reported model. These demonstrated the usefulness and efficiency of the applied method for finding partial differential equations' solitary wave solutions. Additionally, utilizing Maple mathematical software in both 2D and 3D as well as the contour plots, some of the calculated solutions are plotted to comprehend the physical structures of the investigated model.