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

Open Physics

Aydemir Tuğba¹  Akçaği Şamil² 

[1] Institute of Natural Sciences, Sakarya University, Sakarya, Turkey;The Faculty of Economics and Administrative Sciences, Bilecik Şeyh Edebali University, Bilecik, Turkey;

关键词: the (g′/g)-expansion method;    the modified extended tanh function method;    the lonngren wave equation;    an exact solution;    02.30.jr;    02.70.wz;    02.60.lj;    03.65.ge;   

DOI  :  10.1515/phys-2016-0006

来源: DOAJ

【 摘 要 】

In this paper, firstly, we give a connection between well known and commonly used methods called the (G'G)$\left( {{{G'} \over G}} \right)$ -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)$\left( {{{G'} \over G}} \right)$ - 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)$\left( {{{G'} \over G}} \right)$-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)$\left( {{{G'} \over G}} \right)$-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.

【 授权许可】

Unknown