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Open Physics
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Open Physics
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Unification of all hyperbolic tangent function methods

Authors: Gozukizil, Omer Faruk; Akcagil, Samil; Aydemir, Tugba;

Unification of all hyperbolic tangent function methods

Abstract

Abstract Over the last twenty years, several “different” hyperbolic tangent function methods have been proposed to search solutions for nonlinear partial differential equations (NPDEs). The most common of these methods were the tanh-function method, the extended tanh-function method, the modified extended tanh-function method, and the complex tanh-function method. Besides the excellent sides of these methods, weaknesses and deficiencies of each method were encountered. The authors realized that they did not actually give “very different and comprehensive results”, and some of them are even unnecessary. Therefore, these methods were analysed and significant findings obtained. Firstly, they compared all of these methods with each other and gave the connections between them; and secondly, they proposed a more general method to obtain many more solutions for NPDEs, some of which having never been obtained before, and thus to overcome weaknesses and deficiencies of existing hyperbolic tangent function methods in the literature. This new method, named as the unified method, provides many more solutions in a straightforward, concise and elegant manner without reproducing a lot of different forms of the same solution. Lastly, they demonstrate the effectiveness of the unifed tanh method by seeking more exact solutions of the Rabinovich wave equation which were not obtained before.

Country
Turkey
Related Organizations
Keywords

02.60.lj, 05.45.yv, the modified extended tanh-function method, the tanh-function method, Physics, QC1-999, the extended tanh-function method, 02.70.wz, The modified extended tanh-function method, The extended tanh-function method, the rabinovich wave equation, 03.65.ge, The complex tanhfunction method, The tanh-function method, The Rabinovich wave equation, The unified method, the complex tanhfunction method, the unified method, 02.60.cb

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
34
Top 10%
Top 10%
Average
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gold