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.
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.
Primary Language | English |
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Subjects | Numerical Analysis |
Journal Section | Research Articles |
Authors | |
Early Pub Date | July 14, 2024 |
Publication Date | July 15, 2024 |
Submission Date | November 25, 2023 |
Acceptance Date | June 6, 2024 |
Published in Issue | Year 2024 Volume: 26 Issue: 2 |