Exact wave solutions to the simplified modified Camassa-Holm equation in mathematical physics

Abstract

In this article, we consider the exact solutions to the simplified modified Camassa-Holm (SMCH) equation which has many potential applications in mathematical physics and engineering sciences. We examine the exact travelling wave solutions by means of the modified simple equation (MSE) method by making use of travelling transformation. The attained solutions are in the form of trigonometric and hyperbolic functions. We demonstrate that the method is more general, straightforward and powerful and can be used to examine more general travelling wave solutions of various kinds of fractional nonlinear differential equations arising in mathematical physics and better than other method. Finally, we show the graphical representation and discuss the physical significance of the obtained solutions for its definite values of the involved parameters through depicting 3D and 2D figures in order to know the physical phenomena.

Keywords

• nonlinear evolution equations
• simplified modified camassa-holm equation
• travelling transformation
• modified simple equation method