(2+1)-Boyutlu Ablowitz-Kaup-Newell-Segur Denklemi için Gezici Dalga Çözümlerinin İncelenmesi

Year 2025, Volume: 3 Issue: 1, 50 - 57, 30.06.2025

Hülya Durur

https://doi.org/10.63063/jsat.1678536

Abstract

Bu çalışmada, geliştirilmiş alt denklem yöntemi (2+1)-Ablowitz-Kaup-Newell-Segur (AKNS) denklemine uygulanmıştır. Bu analitik yöntemle trigonometrik, hiperbolik ve rasyonel tipte çözümleri üretilmiştir. Durağan dalgayı temsil eden kontur, 3 boyutlu ve 2 boyutlu grafikleri bu çözümlerdeki sabitlere rastgele değerler verilerek çizilir. Sembolik hesaplama kullanılarak, bu yöntemin doğrusal olmayan evrim denklemlerinin çözümlerini üretmek için etkili, güçlü ve güvenilir bir araç olduğu gösterilmiştir.

Keywords

Geliştirilmiş alt denklem metodu, doğrusal olmayan evrim denklemi, tam çözüm.

Thanks

This work was created as a part of the research process on "Travelling Wave Solutions of Nonlinear Partial Differential Equations" carried out in the Department of Mathematics, Faculty of Arts and Sciences, Kafkas University. The author would like to express her sincere gratitude to Kafkas University for their great contribution to the success of the study

Investigation of Travelling Wave Solutions for the (2+1)-Dimensional Ablowitz-Kaup-Newell-Segur Equation

Abstract

In this study, modified sub equation method was applied to the (2+1)-Ablowitz-Kaup-Newell-Segur (AKNS) equation. This analytical method, trigonometric, hyperbolic and rational type solutions have been produced. Contour, 3D and 2D graphs representing stationary wave are drawn by giving random values to the constants in these solutions. Using symbolic computation, this method is shown to be an effective, powerful and reliable tool for generating nonlinear evolution equations (NEDEs).

Keywords

Modified sub equation method, nonlinear evolution equation, exact solution.

Thanks

This work was created as a part of the research process on "Travelling Wave Solutions of Nonlinear Partial Differential Equations" carried out in the Department of Mathematics, Faculty of Arts and Sciences, Kafkas University. The author would like to express her sincere gratitude to Kafkas University for their great contribution to the success of the study

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