A generalized (G′G)-expansion method for the mKdV equation with variable coefficients

In this Letter, a generalized (G′G)-expansion method is proposed to seek exact solutions of nonlinear evolution equations. Being concise and straightforward, this method is applied to the mKdV equation with variable coefficients. As a result, hyperbolic function solution, trigonometric function solution and rational solution with parameters are obtained. When the parameters are taken as special values, two known kink-type solitary wave solutions are derived from the hyperbolic function solution. It is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations in mathematical physics.