A connection between the (G'/G)-expansion method and the truncated Painlevé expansion method and its application to the mKdV equation

Recently the (G'/G)-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the (G'/G)-expansion method is a special form of the truncated Painlevé expansion method by introducing an intermediate expansion method. Then the generalized (G'/G)--(G'/G) expansion method is naturally derived from the standpoint of the nonstandard truncated Painlevé expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the (G'/G)-expansion method.