Traveling wave solutions for the mKdV equation and the Gardner equations by new approach of the generalized (G′/G)-expansion method

Abstract

In this paper, we demonstrate the effectiveness of the new generalized (G′/G)-expansion method by seeking more exact solutions via the mKdV equation and the Gardner equations. The method is direct, concise and simple to implement compared to other existing methods. The traveling wave solutions obtained by this method are expressed in terms of hyperbolic, trigonometric and rational functions. The method shows a wide application for handling nonlinear wave equations. Moreover, the method reduces the large amount of calculations.

Keywords

• New generalized (G′/G)-expansion method
• mKdV equation
• Gardner equation
• Traveling wave solutions
• Solitary wave solutions