A Generalized (3+1)-Dimensional Nonlinear Wave Equation in Liquid with Gas Bubbles: Symmetry Reductions; Exact Solutions; Conservation Laws

Abstract

The analysis of a generalised (3+1)-dimensional nonlinear wave equation that simulates a variety of nonlinear processes that occur in liquids including gas bubbles will be performed. After some cosmetic adjustments to the underlying equation, this generalised (3+1)-dimensional nonlinear wave equation naturally degenerates into the (3+1)-dimensional Kadomtsev-Petviashvili equation, the (3+1)-dimensional nonlinear wave equation, and the Korteweg-de Vries equation. To completely investigate this fundamental equation, a clear and rigorous technique is used. In order to obtain innovative symmetry reductions, group invariant solutions, conservation laws, and eventually kink wave solutions, the Lie symmetry, multiplier, and simplest equation methods are used. Complex waves and their dealing dynamics in fluids can be well imitated by the verdicts.