Jacobi Elliptic Function Solutions of Space-Time Fractional Symmetric Regularized Long Wave Equation

Abstract

In this paper, by using a direct method based on the Jacobi elliptic functions, the exact solutions of the space-time fractional symmetric regularized long wave (SRLW) equation have been obtained. The elliptic function solutions of a nonlinear ordinary differential (auxiliary) equation $\left({dF}/{d \xi}\right) ^{2} = PF^{4} (\xi)+QF^{2} (\xi) + R$ have also been examined. Besides, the solutions have been found in general form including rational, trigonometric and hyperbolic functions. Moreover, the complex valued solutions, periodic solutions, and soliton solutions, have also been gained. Some solutions have been illustrated by the graphics.