New periodic solitary wave solutions for the (3+1)-dimensional generalized shallow water equation

Abstract

Many important physical situations such as fluid flows, plasma physics and solid-state physics have been described by (3+1)-dimensional generalized shallow water equation. In this article, we construct new periodic solitary wave solutions for the (3+1)-dimensional generalized shallow water equation by using the auto-Backlund transformation and a direct test function. These obtained new periodic solitary wave solutions enrich the solution structure. Evidently, with the help of symbolic computation, the physical structure for these periodic solitary wave solutions is presented with some figures. The direct test function approach can be also applied to solve other nonlinear differential equations.