Dynamics of Solitary Waves and Periodic Waves in a (3 + 1)-Dimensional Nonlinear Evolution Equation

Abstract

The Hirota bilinear method is applied to a generalised (3 + 1)-dimensional nonlinear evolution equation. Using the Riemann theta function, we construct periodic wave solutions of the Eq. (1.1) and discuss their properties. Graphic examples show the propagation of the corresponding waves for different sets of parameters. We also study the asymptotic of periodic waves and their relation with solution solutions.