New F Expansion Method and Its Applications to Modified KdV Equation

Abstract

In this paper, the new $F$-expansion method is proposed for constructing more general exact solutions nonlinear evolution equation with the aid of symbolic computation. By using this method, we have successfully obtained some travelling wave solutions of the modified KdV Equation. These exact solutions include the hyperbolic function solutions, trigonometric function solutions, rational function solutions and Jacobi elliptic function solutions. Also it is shown that the proposed method is efficient for solving nonlinear evolution equations in mathematical physics and in engineering.