Determining new soliton solutions for a generalized nonlinear evolution equation using an effective analytical method

In this paper, a generalized (3 + 1)-dimensional nonlinear evolution equation (NLEE) is proposed and examined. This investigated NLEE is undoubtedly a robust mathematical model in real-world applications. Because several essential and commonly used relative differential equations can be obtained by considering some specific choices in the given general form. In this way, many new solitary wave solutions are formally obtained via the generalized exponential rational function method (GERFM). The general idea of solving the equation in this method is to use an appropriate variable change that can transform the given partial differential equation into an ordinary differential equation. We then provide a general symbolic form for the solutions and determine the solution of the equation. To understand the dynamic concepts of numerical solutions better, several numerical simulations are included. The dependence of the properties of the solutions on the selection of the parameters in the equation can be examined in the results. Finally, the results verify the efficiency and reliability of the considered method.