A New Algebraic Method and Its Application to Nonlinear Klein-Gordon Equation

In terms of the solutions of the generalized Riccati equation,a new algebraic method, which contains the terms of radical expression of functions f(ξ), is constructed to explorethe new exact solutions for nonlinear evolution equations.Being concise and straightforward, the method is applied tononlinear Klein-Gordon equation, and some new exact solutionsof the system are obtained. The method is of important significance in exploring exact solutions for other nonlinear evolution equations.