New solitary wave solutions and stability analysis for the generalized (3 + 1)-dimensional nonlinear wave equation in liquid with gas bubbles

Abstract

In this study, solitary wave solutions for the generalized (3 + 1)-dimensional nonlinear wave equation (NLWE) are extracted using a new generalized exponential rational function method (GERFM). Numerous nonlinear behaviors in liquids with gas bubbles are described by this equation. The suggested method is used to derive the various kinds of new accurate soliton solutions for the equation. Also, the physical interpretations of some obtained solutions are represented. In addition, a modulational instability analysis framework is used to look at the system’s stability.