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

Yıl 2024, , 242 - 247, 27.02.2024

Melih Çınar

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

Öz

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.

Anahtar Kelimeler

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

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

• 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
• 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
• Braun, M. (1983b). Differential Equations and Their Applications: An Introduction to Applied Mathematics. In Springer eBooks. USA. https://doi.org/10.1007/978-1-4612-4360-1
• Cinar, M., Secer, A., & Bayram, M. (2022). Analytical solutions of (2+ 1)-dimensional Calogero-Bogoyavlenskii-Schiff equation in fluid mechanics/plasma physics using the New Kudryashov method. Physica Scripta, 97(9), 094002. https://doi.org/10.1088/1402-4896/ac883f
• Cinar, M., Secer, A., Ozisik, M., & Bayram, M. (2023). Optical soliton solutions of (1+ 1)-and (2+ 1)-dimensional generalized Sasa–Satsuma equations using new Kudryashov method. International Journal of Geometric Methods in Modern Physics, 20(02), 2350034. https://doi.org/10.1142/S0219887823500342
• Das, S. E. (2022). Retrieval of soliton solutions of (1+ 1)-dimensional non-linear telegraph equation. Thermal Science, 26(Spec. issue 2), 801-810. https://doi.org/10.2298/TSCI22S2801D
• Davis, J. L. (2012). Wave propagation in electromagnetic media. Springer Science & Business Media. Debnath, L. (2012). Nonlinear partial differential equations for scientists and engineers. In Birkhäuser Boston eBooks. https://doi.org/10.1007/978-0-8176-8265-1
• Farlow, S. J. (2012). Partial Differential Equations for Scientists and Engineers. Dover Publications. Li, L., Xie, Y., & Mei, L. (2021). Multiple-order rogue waves for the generalized (2+1)-dimensional Kadomtsev–Petviashvili equation. Applied Mathematics Letters, 107079. http://dx.doi.org/10.1016/j.aml.2021.107079 Ma, H., Mao, X., & Deng, A. (2023). Resonance solutions and hybrid solutions of an extended (2+1)-dimensional Kadomtsev–Petviashvili equation in fluid mechanics. https://doi.org/10.1007/s11071-023-08569-6
• Malik, S., Almusawa, H., Kumar, S., Wazwaz, A. M., & Osman, M. S. (2021). A (2+ 1)-dimensional Kadomtsev–Petviashvili equation with competing dispersion effect: Painlevé analysis, dynamical behavior and invariant solutions. Results in Physics, 23, 104043. https://doi.org/10.1016/j.rinp.2021.104043
• Mohanty, S. K., Kravchenko, O. V., Deka, M. Kr., Dev, A. N., & Churikov, D. V. (2023). The exact solutions of the 2+1–dimensional Kadomtsev–Petviashvili equation with variable coefficients by extended generalized G′G-expansion method. Journal of King Saud University - Science, 35(1), 102358. https://doi.org/10.1016/j.jksus.2022.102358
• Ozisik, M., Secer A., Bayram, M., Yusuf A., & Sulaiman T. A. (2023). Soliton solutions of the (2+1)-dimensional Kadomtsev–Petviashvili equation via two different integration schemes. International Journal of Modern Physics B, 2350212. http://doi.org/10.1142/s0217979223502120
• Wazwaz, A. (2022). Painlevé integrability and lump solutions for two extended (3+1)- and (2+1)-dimensional Kadomtsev–Petviashvili equations. Nonlinear Dynamics, 111(4), 3623–3632. https://doi.org/10.1007/s11071-022-08074-2
• Weigand, B. (2015). Analytical methods for heat transfer and fluid flow problems. Springer International Publishing. USA. https://doi.org/10.1007/978-3-662-46593-6