An Investigation for Soliton Solutions of the Extended (2+1)-Dimensional Kadomtsev–Petviashvili Equation

Year 2024, Volume: 24 Issue: 1, 242 - 247, 27.02.2024

Melih Çınar

https://doi.org/10.35414/akufemubid.1333304

Abstract

This article presents an investigation for soliton solutions of the extended (2+1)-dimensional Kadomtsev–Petviashvili equation which describes wave behavior in shallow water. We utilize the unified Riccati equation expansion method. By employing the powerful method, many soliton solutions are successfully derived, and it is verified by Wolfram Mathematica that the solutions satisfy the main equation. Additionally, Matlab is utilized to generate plots and examine the properties of the obtained solitons. The results reveal that the considered equation exhibits a wide range of soliton solutions, including dark, bright, singular, and periodic solutions. This comprehensive investigation of soliton solutions for the Kadomtsev–Petviashvili equation holds significant relevance in various fields such as oceanography and nonlinear optics, contributing to practical applications.

Keywords

nonlinear optics, unified Riccati equation expansion method, shallow water waves, Kadomtsev–Petviashvili Equation

Genişletilmiş (2+1)-boyutlu Kadomtsev–Petviashvili Denkleminin Soliton Çözümlerinin Araştırılması

Abstract

Bu makale, sığ suda dalga davranışını tanımlayan genişletilmiş (2+1) boyutlu Kadomtsev–Petviashvili denkleminin soliton çözümlerinin birleşik Riccati denklemi genişletme yöntemini kullanarak bir araştırmasını sunmaktadır. Söz konusu yöntem kullanılarak, birçok soliton çözümü başarıyla elde edildi ve çözümlerin ana denklemi sağladığı Wolfram Mathematica programı kullanılarak doğrulandı. Grafikler oluşturmak ve elde edilen solitonların özelliklerini incelemek için Matlab programı kullanıldı. Sonuçlar, ele alınan denklemin karanlık, parlak, tekil ve periyodik çözümler dahil olmak üzere çok çeşitli soliton çözümler sergilediğini ortaya koymaktadır. Kadomtsev-Petviashvili denklemi için soliton çözümlerinin bu kapsamlı araştırması, pratik uygulamalara katkıda bulunan oşinografi ve doğrusal olmayan optik gibi çeşitli alanlarda önemli bir öneme sahip olduğu için bu alanlardaki ileri çalışmalara ışık tutacağı öngörülmektedir.

Keywords

Doğrusal olmayan optik, Birleşik Riccati denklemi genişletme yöntemini, Sığ su dalgaları, Kadomtsev–Petviashvili Denklemi

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