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Journals / An International Journal of Optimization and Control: Theories & Applications (IJOCTA) / 2017 / Cilt: 7 - Sayı: 3

Special issue of the 2nd International Conference on Computational Mathematics and Engineering Sciences (CMES2017)

Hasan c BULUT
Yusuf b GUREFE
Tolga AKTURK
Pages
1234–1239
Publication Date
2022-10-11
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

According these results, one can easily see that this method is very effective mathematical tool for the (N+1)-dimensional nonlinear physical problems.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, a new approach that assumes u f u   cos  and u f u   sinh   is applied to construct the traveling wave solutions of the (N + 1)-dimensional double sine-Gordon and (N + 1)-dimensional double sinh-coshGordon equations.
📊
Key Findings & Data:Some new elliptic integral function solutions are respectively obtained by this method, and then these solutions are converted into the Jacobi elliptic function solutions.
💡
Conclusion & Impact:According these results, one can easily see that this method is very effective mathematical tool for the (N+1)-dimensional nonlinear physical problems.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study, a new approach that assumes u f u   cos  and u f u   sinh   is applied to construct the traveling wave solutions of the (N + 1)-dimensional double sine-Gordon and (N + 1)-dimensional double sinh-coshGordon equations. Some new elliptic integral function solutions are respectively obtained by this method, and then these solutions are converted into the Jacobi elliptic function solutions. According these results, one can easily see that this method is very effective mathematical tool for the (N+1)-dimensional nonlinear physical problems.

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Cite This Article

BULUT, H. C., GUREFE, Y. B., AKTURK, T. (2022). Special issue of the 2nd International Conference on Computational Mathematics and Engineering Sciences (CMES2017). An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 7 - Sayı: 3, 1234–1239. https://ajindex.com/articles/440666

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References (1)

  1. Liu, C. S., (2005). Trial equation method and its applications to nonlinear evolution equations, Acta. Phys. Sin. 54, 2505-2509 [2] 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, 16 pages [3] Pandir, Y., Gurefe, Y., & Misirli, E., (2013). Classification of exact solutions to the generalized Kadomtsev- Petviashvili equation, Phys. Scr. 87, 12 pages [4] Porubov, A.V., & Velarde, M.G., (1999). Exact periodic solutions of the complex Ginzburg-Landau equation, J. Math. Phys. 40(2), 884-896 [5] Fan, E., (2000). Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A 277(4), 212-218 [6] Kudryashov, N. A., (2012). One method for finding exact solutions of nonlinear differential equations, Commun. Nonl. Sci. Numer. Simul. 17, 2248-2253 [7] Li, J.B., (2007). Exact traveling wave solutions and dynamical behavior for the (n + 1)-dimensional multiple sine-Gordon equation, Sci. in China Ser. A: Math. 50(2), 153-164 [8] Lee, J., & Sakhtivel, R., (2010). Travelling wave solutions for (N+1)-dimensional nonlinear evolution equations, Pramana-J. Phys. 75(4), 565- 578 [9] Wang, D.S., Yan Z., & Li H., (2008). Some special types of solutions of a class of the (N+1)- dimensional nonlinear wave equation, Comput. Math. Appl. 56(6), 1569-1579 [10] Shen, G., Sun, Y., & Xiong, Y., (2013). New travelling-wave solutions for Dodd-Bullough equation, J. Appl. Math. 2013, Article ID.364718, 5 pages [11] Sun, Y., (2014). New travelling wave solutions for Sine-Gordon equation, J. Appl. Math. 2014, Article ID.841416, 4 pages [12] Bulut, H., Akturk, T., & Gurefe, Y., (2014). Traveling wave solutions of the (N+1)-dimensional sin-cosine-Gordon equation, AIP Conference Proceedings, 1637(1), 145-149 [13] Bulut, H., Akturk, T., & Gurefe, Y., (2015). An application of the new function method to the generalized double sinh-Gordon equation, AIP Conference Proceedings, 1648(370014), 4 pages [14] Akturk, T., (2015). Determining the exact solutions of some nonlinear partial differential equations by trial equation methods, Firat University, PhD Thesis