F -Expansion Method and New Exact Solutions of the Schrödinger-KdV Equation

Abstract EN

F -expansion method is proposed to seek exact solutions of nonlinear evolution equations.

With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method.

A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions.

When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively.

The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics.