we apply this method to the KdV-mKdV equation, the double sine-Gordon equation and the BBM equation, and some new Jacobian elliptic function solutions of them are derived, The method can be applied to other nonlinear evolution equations in mathematical physics.

Solving the KdV-mKdV equation by the bilinear derivative method;

The exact expression of multi-soliton solutions to the KdV-mKdV equation is obtained by Hirota method and the interaction process of multi-soliton is described by numerical figures.

New exact solitary wave solutions of the Burgers equation,combined KdV-mKdV equation and Fisher equation are constructed by replacing the tanh-function with the combinations of the exponential functions.

In order to keep long-time numerical behavior satisfactory,we consider the multi-symplectic formulations of the generalized KdV-mKdV equation with initial value condition in the Hamilton space.

Using direct integration method generalized KDV-MKDV equation was converted the equation into a first-order nonlinear ordinary differential equation,then some new exact solutions were got using undetermined coefficient method,the exact solutiobns were also got using the method that,the assumption transformation was firstly done,then trial function was selected.