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Journals / Karaelmas Fen ve Mühendislik Dergisi / 2018 / Cilt: 8 Sayı: 2

On the Lie symmetry analysis and traveling wave solutions of time fractional fifth-order modified Sawada-Kotera equation

Zaman Kesirli Beşinci Mertebeden Modifiye Edilmiş Sawada-Kotera Denkleminin Lie Simetri Analizi ve İlerleyen Dalga Çözümleri

Emrullah Yasar(Department of Mathematics, Faculty of Arts and Sciences, Uludag University, Bursa, Turkey)
Yakup Yıldırım(Department of Mathematics, Faculty of Arts and Sciences, Uludag University, Bursa, Turkey)
Pages
411–416
Publication Date
2018-06-01
DOI
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AI Summary & Key Takeaways

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

In addition, we construct some exact traveling solutions for the FMSK using the sub-equation method.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study Lie symmetry analysis of the time fractional fifth-order modified Sawada-Kotera equation FMSK with Riemann-Liouville derivative.
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Key Findings & Data:Applying the adapted the Lie group theory to the equation under study, two dimensional Lie algebra is deduced.
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Conclusion & Impact:In addition, we construct some exact traveling solutions for the FMSK using the sub-equation method.
🔬Design:Makale
📍Scope:Comprehensive Sample
⚙️Variables:Lie simetri · Riemann-Liouville türevi · Zaman kesirli modifiye edilmiş Sawada-Kotera denklemi

Abstract

In this paper, we study Lie symmetry analysis of the time fractional fifth-order modified Sawada-Kotera equation FMSK with Riemann-Liouville derivative. Applying the adapted the Lie group theory to the equation under study, two dimensional Lie algebra is deduced. Using the obtained nontrivial Lie point symmetry, it is shown that the equation can be converted into a nonlinear fifth order ordinary differential equation of fractional order in the meaning of the Erdelyi-Kober fractional derivative operator. In addition, we construct some exact traveling solutions for the FMSK using the sub-equation method.

Özet

Bu makalede Riemann-Liouville türevine sahip beşinci mertebeden zaman kesirli modifiye edilmiş Sawada-Kotera denkleminin Lie grup analizi araştırılmıştır. Lie grup teorisinin denkleme uygulanmasıyla iki boyutlu Lie cebri elde edilmiştir. Aşikar olmayan Lie simetrisinin kullanılmasıyla denklemin Erdelyi-Kober kesirli türev operatörü cinsinden beşinci mertebeden kesirli adi diferensiyel denkleme dönüştürülebileceği gösterilmiştir. Bunun yanında alt-denklem metodu kullanılarak denklemin bazı tam ilerleyen dalga çözümlerine ulaşılmıştır

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Cite This Article

Yasar, E., Yıldırım, Y. (2018). On the Lie symmetry analysis and traveling wave solutions of time fractional fifth-order modified Sawada-Kotera equation. Karaelmas Fen ve Mühendislik Dergisi, Cilt: 8 Sayı: 2, 411–416. https://ajindex.com/articles/1152515

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