AccScience Publishing / IJOCTA / Volume 7 / Issue 3 / DOI: 10.11121/ijocta.01.2017.00488
RESEARCH ARTICLE

An application of the new function method to the Zhiber–Shabat equation

Tolga Akturk1* Yusuf Gurefe2 Yusuf Pandır3
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1 Department of Mathematics and Science Education, Faculty of Education, Ordu University, Turkey
2 Department of Econometrics, Faculty of Economics and Administrative Sciences, Usak University, Turkey
3 Department of Mathematics, Faculty of Science and Arts, Bozok University, Turkey
IJOCTA 2017, 7(3), 271–274; https://doi.org/10.11121/ijocta.01.2017.00488
Submitted: 14 June 2017 | Accepted: 16 September 2017 | Published: 28 October 2017
© 2017 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract

This paper applies a new approach including the trial equation based on the exponential function in order to find new traveling wave solutions to Zhiber-Shabat equation. By the using of this method, we obtain a new elliptic integral function solution. Also, this solution can be converted into Jacobi elliptic functions solution by a simple transformation.

Keywords
New function method
Zhiber-Shabat equation
Elliptic integral function solution
Conflict of interest
The authors declare they have no competing interests.
References

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[4] Sun, Y., (2014).New travelling wave solutions for  Sine-Gordon equation, J. Appl. Math. 2014, pp. 4 

[5] Bulut, H., Akturk, T., & Gurefe, Y.,  (2014).Travelling wave solutions of the (N+1)- dimensional sine-cosine-Gordon equation, AIP  Conf. Proc. pp. 5 

[6] Kudryashov, N. A., (2012).One method for finding  exact solutions of nonlinear differential equations,  Commun. Nonl. Sci. Numer. Simul. 17, 2248-2253 

[7] Tang, Y., Xu, W., Shen, J., & Gao, L.,  (2007).Bifurcations of traveling wave solutions for  Zhiber–Shabat equation, Nonlinear Analy.. 67, 648- 656  [8] Chen, Huang, W., & Li, J., (2009).Qualitative  behavior and exact travelling wave solutions of the Zhiber_Shabat equation, J. Comp. and Appl. Mat. 230, 559-569

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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing