Rasyonel sine-Gordon metodu ile (2+1) boyutlu Zoomeron denkleminin analitik çözümü

Abstract

Mevcut çalışma matematiğin fiziğin önemli modellerinden biri olan Zoomeron denkleminin çözümü ile ilgilidir. Bu çalışmada denklemin çözümü için rasyonel Sine-Gordon açılım metodu kullanılıp analitik çözümler elde edildi. Diğer metotlara göre bu metot oldukça etkili olup istenilen sonuçlar elde edildi. Bununla birlikte Matematika programı ile çözümlerin iki ve üç boyutlu uzayda geometrik yorumu yapılmıştır.

Keywords

• Rasyonel Sine-Gordon açılım metodu
• Zoomeron denklemi
• Analitik metot

Analytical solution of the (2+1)-dimensional Zoomeron equation by rational sine-Gordon Method

Abstract

The current study is about the solution of the Zoomeron equation, one of the important models of mathematics and physics. In this study, the rational Sine-Gordon expansion method (RSGEM) is used to obtain various analytical solutions of the model. Compared to other methods, this method is quite effective and the desired results were obtained. Although there are many analytical solutions to the model used in the literature, we present rational type solutions for the first time with this method. We obtained rational hyperbolic function solutions, and also classified all soliton solutions (kink-like, kink, singular kink, anti-kink, dark, bright). In addition, geometric representations of the solutions in two-, and three-dimensional space and contour shape are made with the Mathematica software program.

Keywords

• RSGEM
• Zoomeron Equation
• Analytical Method

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