EXAMINATION OF KRAENKEL-MANNA-MERLE SYSTEM BY SINE-GORDON EXPANSION METHOD

Year 2022, Volume: 8 Issue: 2, 54 - 59, 30.12.2022

Şeyma Tülüce Demiray , Uğur Bayrakcı

https://doi.org/10.22531/muglajsci.1161678

Abstract

In this study, Kraenkel-Manna-Merle (KMM) system is discussed. Sine-Gordon expansion method (SGEM), which is one of the solution methods of nonlinear evolution equations (NLEEs), has been applied to this system. Thus, by applying this method for the first time, some dark soliton, bright soliton, and dark-bright soliton solutions of the KMM system have been obtained. In addition, by giving specific values to the achieved solutions, 2D and 3D graphics of the solutions were plotted by way of the Wolfram Mathematica 12 program.

Keywords

Kraenkel-Manna-Merle System, mathematica, SGEM

KRAENKEL-MANNA-MERLE SİSTEMİNİN SGEM YOLUYLA İNCELENMESİ

Abstract

Bu çalışmada, Kraenkel-Manna-Merle sistemi ele alınmıştır. Doğrusal olmayan evrim denklemlerinin çözüm yöntemlerinden biri olan sinüs-Gordon açılım yöntemi bu sisteme uygulanmıştır. Böylece ilk kez bu yöntem uygulanarak KMM sisteminin bazı dark soliton, bright soliton ve dark-bright soliton çözümleri elde edilmiştir. Ayrıca elde edilen çözümlere belirli değerler verilerek Wolfram Mathematica 12 programı aracılığıyla çözümlerin 2 boyutlu ve 3 boyutlu grafikleri çizilmiştir.

Keywords

Kraenkel-Manna-Merle Sistemi, mathematica, SGEM

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