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

Tolga Aktürk, Yusuf Gürefe, Yusuf Pandır

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.

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References


Liu, C. S. (2005). Trial equation method and its applications to nonlinear evolution equations, Acta. Phys. Sin. 54, 2505-2509.

Pandir, Y., Gurefe, Y., Kadak, U., & Misirli, E., (2012).Classification of exact solutions for some nonlinear partial differential equations with generalized evolution, Abstr. Appl. Anal. 2012, pp. 16

Shen, G., Sun, Y., & Xiong, Y., (2013). New travelling-wave solutions for Dodd-Bullough equation, J. Appl. Math. 2013, pp. 5

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

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

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

Tang, Y., Xu, W., Shen, J., & Gao, L., (2007).Bifurcations of traveling wave solutions for Zhiber–Shabat equation, Nonlinear Analy.. 67, 648-656

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




DOI: http://dx.doi.org/10.11121/ijocta.01.2017.00488

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Copyright (c) 2017 TOLGA AKTÜRK, YUSUF GÜREFE, YUSUF PANDIR

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