The improved F-expansion method and its applications

The F-expansion method has been developed recently, and is a useful tool to derive the periodic wave solutions expressed by Jacobi elliptic functions for the nonlinear evolution equations. In this Letter, the improved F-expansion method, and the condition which the improved F-expansion method can be used, are introduced. As the illustrative example, the exact solutions expressed by Jacobi elliptic functions, Weierstrass elliptic function, triangle functions, hyperbolic functions and other type of functions for the generalized Hirota–Satsuma coupled KdV equation are derived.