Süper İletkenlik Alanında Yeni Dalga Çözümleri

Abstract

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.

Keywords

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

The New Wave Solutions in the Field of Superconductivity

Abstract

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.

Keywords

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

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