By means of the improved double functions method, many kinds of exact travelling wave solutions for a class of nonlinear evolution equations are obtained, which contain soliton wave solutions and periodic solutions.

Based on the homogeneous balance method and trial function method,two trial func- tion methods of exponential functions are presented.

Based on the trial function method,a new trial function method combined with exponential functions is presented and applied to the nonlinear discrete system.

The paper concerns with Fisher equation,and the authors construct some new exact solutions by using the trial function method.

By utilizing the auxiliary ordinary differential equation and its solutions,the first kind and second kind of KdV equation with variable coefficients were investigated by means of the extended tanh-function method,and abundant new exact solitary wave solutions were obtained under certain conditions.

With the further improved hyperbolic functions method,the new exact soliton solutions for the equation of nonlinear vibrating string are obtained,which include kink soliton solution and new soliton-like solutions.

With the help of the further improved hyperbolic functions method,the new discrete soliton solutions for the discrete nonlinear Schrdinger equation are obtained,which include discrete kink-type soliton solution,bell-type soliton solution and new formal soliton-like solutions.