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' \over 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' \over 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' \over G )-expansion method gives neither all of 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' \over 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.
- Publication:
-
Open Physics
- Pub Date:
- January 2016
- DOI:
- 10.1515/phys-2016-0006
- Bibcode:
- 2016OPhy...14....6A
- Keywords:
-
- The ({G'}\over G)-expansion method;
- The modified extended tanh function method;
- The Lonngren wave equation;
- An exact solution;
- The (G‧/G)-expansion method