The Two-Variable (G `/G, 1/G)-Expansion Method for Solving the Nonlinear KdV-mKdV Equation

We apply the two-variable (G'/G, 1/G)-expansion method to construct new exact traveling wave solutions with parameters of the nonlinear (1 + 1)-dimensional KdV-mKdV equation. This method can be thought of as the generalization of the well-known (G'/G)-expansion method given recently by M. Wang et al. When the parameters are replaced by special values, the well-known solitary wave solutions of this equation are rediscovered from the traveling waves. It is shown that the proposed method provides a more general powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.