Comparison between the (G'/G) - expansion method and the modified extended tanh method

Abstract

In this paper, firstly, we give a connection between well known and commonly used methods called the (G'/G) - expansion method and the modified extended tanh method which are often used for finding exact solutions of nonlinear partial differential equations(NPDEs). We demonstrate that giving a convenient transformation and formula, all of the solutions obtained by using the (G'/G) - expansion method can be converted the solutions obtained by using the modified extended tanh method. Secondly, contrary to the assertion in some papers, the (G'/G) - expansion method gives neither all of the the solutions obtained by using the other method nor new solutions for NPDEs. Namely, while the modified extended tanh method gives more solutions in a straightforward, concise and elegant manner without reproducing a lot of different forms of the same solution. On the other hand, the (G'/G) - expansion method provides less solutions in a rather cumbersome form. Lastly, we obtain new exact solutions for the Lonngren wave equation as an illustrative example by using these methods.