Süper İletkenlik Alanında Yeni Dalga Çözümleri

Yıl 2022, Cilt: 11 Sayı: 2, 449 - 458, 30.06.2022

Özlem Kırcı Tolga Aktürk Hasan Bulut

https://doi.org/10.17798/bitlisfen.1020207

Öz

Bu çalışmada, fiziksel anlamda önemli dalga çözümleri olan Landau-Ginzburg-Higgs (LGH) denklemi göz önüne alınmıştır. Belirtilen denklemin çözümleri, süper iletkenliği tanımlamak için, modifiye exponansiyel fonksiyon metodu (MEFM) ile incelenmiştir. Literatürde yer alan çözümler ile kıyaslandığında bu denklemin rasyonel, hiperbolik ve trigonometrik fonksiyon formunda bazı yeni çözümleri elde edilmiştir. Bu yöntemle elde edilen ve nonlineer denklemin gerçek çözümleri olmaya aday olan fonksiyonlar, uygulanan metodun sounda Mathematica programı yardımı ile test edilmiş ve LGH denklemini sağladığı gözlemlenmiştir. Ayrıca bu çözümlerin iki boyutlu ve üç boyutlu grafikleri, yoğunluk ve kontur çizimleri ile birlikte sunulmuştur.

Anahtar Kelimeler

Landau-Ginzburg-Higgs (LGH) denklemi, Modifiye exponansiyel fonksiyon metodu, Dalga çözümleri.

The New Wave Solutions in the Field of Superconductivity

Öz

In this study, the Landau-Ginzburg-Higgs (LGH) equation which has the physically important wave solutions is considered. This equation is discussed via modified exponential function method (MEFM) to describe superconductivity. Some new solutions are discovered in the form of rational, hyperbolic and trigonometric functions when compared with the ones taking part in the literature. The functions which are candidate to be the exact solutions of the nonlinear equation are tested by Mathematica program at the end of the steps of the method and it is observed that they satisfy the LGH equation. Additionally the 2-D and the 3-D graphs accompanying the density and contour plots are illustrated.

Anahtar Kelimeler

Landau-Ginzburg-Higgs (LGH) equation, The modified exponential function method, Wave solutions

Kaynakça

• [1] Xiang T. 2015. A Summary of the Korteweg-de Vries Equation. Institute for Mathematical Sciences, Renmin University of China, Beijing, 100872, China.
• [2] Zayed E.M.E., Alurrfi, K.A.E. 2015. On solving two higher-order nonlinear PDEs describing the propagation of optical pulses in optic fibers using the -expansion method. Ricerche di Mathematica, 64 (1): 167–194.
• [3] Mohyud-Din S.T., Noor Aslam M., Noor Inayat K. 2010. Exp-function method for traveling wave solutions of modified Zakharov-Kuznetsov equation. Journal of King Saud University (Science), 22 (4): 213-216.
• [4] Wazwaz A.M. 2004. The tanh method for traveling wave solutions of nonlinear equations. Applied Mathematics and Computation, 154 (3): 713-723.
• [5] Wang K.J., Wang G.D. 2021. Solitary and periodic wave solutions of the generalized fourth-order Boussinesq equation via He's variational methods. Mathematical Methods in the Applied Sciences, 44 (7): 5617-5625.
• [6] Abdelrahman M.A.E., Sohaly M.A. 2019. On the new wave solutions to the MCH equation. Indian Journal of Physics, 93 (7): 903-911.
• [7] Baskonus H.M., Gomez-Aguilar J.F. 2019. New singular soliton solutions to the longitudinal wave equation in a magneto-electro-elastic circular rod with M-derivative. Modern Physics Letters B, 33 (21).
• [8] Kudryashov N.A. 2010. A note on the -expansion method. Applied Mathematics and Computation, 217 (4): 1755-1758.
• [9] Xian-Lin Y., Jia-Shi T. 2008. Travelling Wave Solutions for Konopelchenko–Dubrovsky Equation Using an Extended sinh-Gordon Equation Expansion Method. Communications in Theoretical Physics, 50 (5): 1047.
• [10] Rezazadeh H., Korkmaz A., Khater M.M.A., Eslami M., Lu D., Attia R.A.M. 2019. New exact traveling wave solutions of biological population model via the extended rational sinh-cosh method and the modified Khater method. Modern Physics Letters B, 33(28): 1950338.
• [11] He J.H. 1999. Variational iteration method – a kind of non-linear analytical technique: some examples. International Journal of Nonlinear Mechanics, 34 (4): 699-708.
• [12] Liu S., Fu Z., Liu S., Zhao Q. 2001. Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Physics Letters A, 289 (1-2): 69-74.
• [13] Zhang S. 2006. New exact solutions of the KdV–Burgers–Kuramoto equation. Physics Letters A, 358 (5-6): 414-420.
• [14] Barman H.K., Akbar M.A., Osman M.S., Nisar K.S., Zakarya M., Abdel-Aty A.H., Eleuch H. 2021. Solutions to the Konopelchenko-Dubrovsky equation and the Landau-Ginzburg-Higgs equation via the generalized Kudryashov technique. Results in Physics, 24: 104092.
• [15] Islam Md.E., Akbar M.A. 2020. Stable wave solutions to the Landau-Ginzburg-Higgs equation and the modified equal width wave equation using the IBSEF method. Arab Journal of Basic and Applied Sciences, 27 (1): 270-278.
• [16] Barman H.K., Aktar M.S., Uddin M.H., Akbar M.A., Baleanu D., Osman M.S. 2021. Physically significant wave solutions to the Riemann wave equations and the Landau-Ginsburg-Higgs equation. Results in Physics, 27, 104517.
• [17] Ghanbari B., Gomez-Aguilar J.F. 2019. Optical soliton solutions of the Ginzburg-Landau equation with conformable derivative and Kerr law nonlinearity. Revista Mexicana de Fisica, 65: 73-81.
• [18] Bekir A., Unsal O. 2013. Exact solutions for a class of nonlinear wave equations by using the first integral method. International Journal of Nonlinear Science, 15 (2): 99–110.
• [19] Iftikhar A., Ghafoor A., Jubair T., Firdous S., Mohyud-Din ST. 2013. The expansion method for travelling wave solutions of (2+1)-dimensional generalized KdV, sine Gordon and Landau-Ginzburg-Higgs equation. Scientific Research and Essays, 8 (28): 1349–1859.
• [20] Islam M.E., Akbar M.A. 2020. Stable wave solutions to the Landau-Ginzburg-Higgs equation and the modified equal width wave equation using the IBSEF method. Arab Journal of Basic and Applied Sciences, 27 (1): 270–8.
• [21] Bulut H., Baskonus H.M. 2016. New Complex Hyperbolic Function Solutions for the (2+1)-Dimensional Dispersive Long Water–Wave System. Mathematical and Computational Applications, 21 (2): 6.