Using expanding method of (G'/G ) to find the travelling wave solutions of nonlinear partial differential equations and solving mkdv equation by this method

Expanding method of (G′/G) can be implemented to nd survey solutions of travelling wave of some nonlinear partial dierential equations. The answers depend on hyperbolic functions, trigonometric functions and rational functions (see [1]). This method, converts nonlinear partial dierential equations into a plane dierential equation. It is possible to use this method to solve integrable equations and non-integrable equations. In this paper, by describing the method we analysis the application of it to solve mkdv equation (see [2-3]). Phenomenon in physics and other elds are often described by nonlinear partial dierential equations. During 40 years ago, nding survey solutions of nonlinear partial dierential equations by implementing dierent methods have been the target of many researchers and the powerful methods of inverse diusion method, homogeneous equilibrium,.expanding method of (G′/G) are proposed that are based on assump- tions that the solutions of travelling wave of nonlinear partial dierential equations can be expressed in (G′/G) by polynomial and G = G(xi)is correct in second order linear ordinary dierential equations (LODE). The degree of polynomial can be obtained by balance between the highest-order derivative of the dependent variable in linear part of the dierential equation with highest-order of dependent variable in nonlinear part that is appeared in ODE.