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


Akçaǧi Ş., Aydemir T.

Open Physics, vol.14, no.1, pp.88-94, 2016 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 1
  • Publication Date: 2016
  • Doi Number: 10.1515/phys-2016-0006
  • Journal Name: Open Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.88-94
  • Keywords: An exact solution, The (G/G)-expansion method, The Lonngren wave equation, The modified extended tanh function method
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

© 2016 Şamil Akçaǧi and Tuǧba Aydemir, published by De Gruyter Open. 2016.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 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.