TY - JOUR T1 - An Investigation for Soliton Solutions of the Extended (2+1)-Dimensional Kadomtsev–Petviashvili Equation TT - Genişletilmiş (2+1)-boyutlu Kadomtsev–Petviashvili Denkleminin Soliton Çözümlerinin Araştırılması AU - Çınar, Melih PY - 2024 DA - February DO - 10.35414/akufemubid.1333304 JF - Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi PB - Afyon Kocatepe University WT - DergiPark SN - 2149-3367 SP - 242 EP - 247 VL - 24 IS - 1 LA - en AB - 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. KW - nonlinear optics KW - unified Riccati equation expansion method KW - shallow water waves KW - Kadomtsev–Petviashvili Equation N2 - 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. CR - Albayrak, P. (2022). Soliton solutions of (2+ 1)-dimensional non-linear reaction-diffusion model via Riccati-Bernoulli approach. Thermal Science, 26(Spec. issue 2), 811-821. https://doi.org/10.2298/TSCI22S2811A CR - Albayrak, P. (2023). Optical solitons of Biswas–Milovic model having spatio-temporal dispersion and parabolic law via a couple of Kudryashov’s schemes. Optik, 279, 170761. https://doi.org/10.1016/j.ijleo.2023.170761 CR - Braun, M. 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Analytical methods for heat transfer and fluid flow problems. Springer International Publishing. USA. https://doi.org/10.1007/978-3-662-46593-6 UR - https://doi.org/10.35414/akufemubid.1333304 L1 - https://dergipark.org.tr/en/download/article-file/3289391 ER -