Diversity of exact solutions to a (3+1)-dimensional nonlinear evolution equation and its reduction

In this paper, a (3+1)-dimensional nonlinear evolution equation and its reduction is studied by use of the Hirota bilinear method and the test function method. With symbolic computation, diversity of exact solutions is obtained by solving the under-determined nonlinear system of algebraic equations for the associated parameters. Finally, analysis and graphical simulation are given to reveal the propagation and dynamical behavior of the solutions.