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

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

Anahtar Kelimeler:

Lie simetri, Riemann-Liouville türevi, Zaman kesirli modifiye edilmiş Sawada-Kotera denklemi, İlerleyen dalga çözümleri

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

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.

Keywords:

Lie symmetry, Riemann-Liouville derivative, Time fractional modified Sawada-Kotera equation, Traveling wave solutions,

PDF

___

Adem, AR., Khalique, CM. 2012. Symmetry reductions, exact solutions and conservation laws of a new coupled KdV system. Commun. Nonlinear Sci. Numer. Simul., 17: 3465-3475.
Adem, AR., Muatjetjeja, B. 2015. Conservation laws and exact solutions for a 2D Zakharov–Kuznetsov equation. App. Math. Lett., 48: 109-117.
Adem, AR., Lü, X. 2016. Travelling wave solutions of a two- dimensional generalized Sawada–Kotera equation. Nonlinear Dyn.,84(2): 915-922.
Adem, AR. 2016. The generalized (1+ 1)-dimensional and (2+ 1)-dimensional Ito equations: multiple exp-function algorithm and multiple wave solutions. Comput. Math. App.,71(6): 1248- 1258.
Bekir, A., Güner, O., Çevikel, AC. 2013a. Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations. Abstr. Appl. Anal., Article ID 426462, 8 pages
Bekir, A. Güner, Ö. 2013b. Exact solutions of nonlinear fractional differential equations by (G’/G)-expansion method. Chin. Phys. B, 22(11): 110-202.
Bekir, A., Güner, Ö. 2014. The-expansion method using modified Riemann--Liouville derivative for some space-time fractional differential equations. Ain Shams Eng. J., 5(3): 959-965.
Bekir, A., Güner, O., Ünsal, O. 2015. The First Integral Method for Exact Solutions of Nonlinear Fractional Differential Equations. J. Comput. Nonlinear Dyn., 10: 021020-1.
Gazizov, RK., Kasatkin, AA., Lukashcuk, SY. 2009. Symmetry properties of fractional diffusion equations. Phys. Scr., T136, 014016.