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

• Published in: Open Physics 2016-01, Vol.14 (1), p.88-94
• Main Authors: Akçaği, Şamil, Aydemir, Tuğba
• Format: Article
• Language: English
• Subjects: 02.30.Jr; 02.60.Lj; 02.70.Wz; 03.65.Ge; An exact solution; expansion method; The; the (g′/g)-expansion method; The Lonngren wave equation; The modified extended tanh function method
• ISSN: 2391-5471; 2391-5471
• DOI: 10.1515/phys-2016-0006

In this paper, firstly, we give a connection between well known and commonly used methods called the -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 - expansion method can be converted the solutions obtained by using the modified extended tanh method. Secondly, contrary to the assertion in some papers, the -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 -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.