Traveling Wave Solutions for the Nonlinear Evolution Equation via the Generalized Riccati Equation and the (G'/G)-Expansion Method

In this article, we investigate the simplified Modified Camassa-Holm (MCH) equation involving parameters by applying the (G'/G)-expansion method together with the generalized Riccati equation. In addition, G'( ) = c + aG( ) + bG ( ) is used, as an auxiliary equation and called generalized Riccati equation, where a, 2 b and c are arbitrary constants. The obtained traveling wave solutions including solitons and periodic solutions are presented through the hyperbolic, the trigonometric and the rational functions. Further, it is important to point out that one of our solutions is in good harmony for a special case with already published results which in turn validates our other solutions. Moreover, the numerical presentations have been demonstrated of some of the solutions with the aid of commercial software Maple. Mathematics Subject Classification: 35K99 35P99 35P05 PACS: 02.30.Jr 05.45.Yv 02.30.Ik