A Generalized Extended (3+1)-Dimensional Nonlinear Evolution Equation with Solitary Wave Solutions: Conserved Vectors and Lie Groups

Abstract This study investigates the dynamical properties of a generalized extended (3+1)-dimensional nonlinear evolution equation. A variety of ansatz strategies will be employed to accomplish this. The initial solution will be the soliton solution or shock wave soliton solution. Furthermore, the singular soliton solution of the extended (3+1)-dimensional nonlinear evolution problem will be presented. Based on the invariance surface condition, we will derive more analytical solutions. Subsequently, we employ the multiplier method to construct conservation laws. Graphical representations of the obtained solutions will be shown based on suitable selections of the arbitrary parameters included in the solutions to enhance comprehension of the underlying physics.