New exact solutions for the space-time fractional Kawahara equation

Abstract

The Kawahara equation is a model of capillary-gravity water wave and plasma waves. In this paper, a direct method based on the Jacobi elliptic functions is presented to get analytical solutions of the space-time fractional Kawahara equation. Moreover, new exact solutions are obtained for a nonlinear ordinary differential equation (dF/d xi)(2) = PF4(xi) + QF(2)(xi) + R, which appears as an auxiliary equation for solving many partial differential equations. Some notes, theorems, and corollaries are also given for this equation. Solving this auxiliary equation, the solutions of the Duffing equation can also be found. Besides, three test examples are presented to illustrate the application of the method and some solutions are demonstrated by the graphics. (C) 2020 Elsevier Inc. All rights reserved.