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

الملخص EN

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.