New Exact Solutions for the Variable-Coefficient Generalized Hirota-Satsuma Coupled KdV System

In this letter, an improved F-expansion method is used to derive the new exact traveling wave solutions expressed by Jacobi elliptical functions for nonlinear evolution equations. The validity and reliability of the method is tested by its applications for the variable-coefficient generalized Hirota-Satsuma coupled KdV system. The method is straightforward, concise and is a promising and powerful method for other nonlinear evolution equations in mathematical physics. As a result, many different classes of solutions are obtained in terms of Jacobi elliptical functions, Weierstrass elliptical function, triangle functions, hyperbolic functions and other types of functions. In limiting cases, solitary wave solutions of the equations are also obtained.