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Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2026 / Cilt: 23 Sayı: 2

Exact Solutions of the Oskolkov Equation in Fluid Dynamics

Akışkanlar Dinamiğinde Oskolkov Denkleminin Tam Çözümleri

Hülya Durur(Ardahan University)0000-0002-9297-6873
Pages
355–361
Publication Date
2023-05-03
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Implemented method is powerful and an effective method to achieve the exact solutions of nonlinear partial differential equations (NPDEs).

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Traveling wave solutions of the Oskolkov equation, which is a model describing the dynamics of an incompressible visco-elastic Kelvin-Voigt fluid, are investigated in this study.
📊
Key Findings & Data:Complex trigonometric and complex hyperbolic solutions of Oskolkov equation are obtained using the sub equation method.
💡
Conclusion & Impact:Implemented method is powerful and an effective method to achieve the exact solutions of nonlinear partial differential equations (NPDEs).
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Alt denklem metodu · Oskolkov denklemi · Lineer olmayan kısmi diferansiyel denklem

Abstract

Traveling wave solutions of the Oskolkov equation, which is a model describing the dynamics of an incompressible visco-elastic Kelvin-Voigt fluid, are investigated in this study. Complex trigonometric and complex hyperbolic solutions of Oskolkov equation are obtained using the sub equation method. In these obtained solutions, graphs are presented by assigning special values to the parameters. The presented graphics are drawn with a computer package program. Implemented method is powerful and an effective method to achieve the exact solutions of nonlinear partial differential equations (NPDEs).

Özet

Bu çalışmada, sıkıştırılamaz bir visko-elastik Kelvin-Voigt akışkanının dinamiklerini tanımlayan bir model olan Oskolkov denkleminin gezici dalga çözümleri araştırıldı. Alt denklem yöntemini kullanarak Oskolkov denkleminin karmaşık trigonometrik ve karmaşık hiperbolik çözümleri elde edildi. Bu elde edilen çözümlerde parametrelere özel değerler atanarak grafikler sunuldu. Sunulan grafikler bir bilgisayar paket programı ile çizildi. Uygulanan yöntem, lineer olmayan kısmi diferansiyel denklemlerin tam çözümlerini üretmek için güçlü ve etkili bir yöntemdir.

🔖

Cite This Article

Durur, H. (2023). Exact Solutions of the Oskolkov Equation in Fluid Dynamics. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 23 Sayı: 2, 355–361. https://doi.org/10.35414/akufemubid.1119363

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References (17)

  1. Kurt, A., Tozar, A., and Tasbozan, O., 2020. Applying the new extended direct algebraic method to solve the equation of obliquely interacting waves in shallow waters. Journal of Ocean University of China, 19(4), 772-780.
  2. Gurefe, Y., Misirli, E., Sonmezoglu, A., and Ekici, M., 2013. Extended trial equation method to generalized nonlinear partial differential equations. Applied Mathematics and Computation, 219(10), 5253-5260.
  3. Chen, C., and Jiang, Y. L., 2018. Simplest equation method for some time-fractional partial differential equations with conformable derivative. Computers & Mathematics with Applications, 75(8), 2978-2988.
  4. Yokuş, A., Durur, H., and Duran, S., 2021. Simulation and refraction event of complex hyperbolic type solitary wave in plasma and optical fiber for the perturbed Chen-Lee-Liu equation. Optical and Quantum Electronics, 53(7), 1-17.
  5. Liu, W., and Chen, K., 2013. The functional variable method for finding exact solutions of some nonlinear time-fractional differential equations. Pramana, 81(3), 377-384.
  6. Zhang, Z., Li, B., Chen, J., and Guo, Q., 2021. Construction of higher-order smooth positons and breather positons via Hirota’s bilinear method. Nonlinear Dynamics, 105(3), 2611-2618.
  7. Duran, S., Yokuş, A., Durur, H., and Kaya, D., 2021. Refraction simulation of internal solitary waves for the fractional Benjamin–Ono equation in fluid dynamics. Modern Physics Letters B, 35(26), 2150363.
  8. Raslan, K. R., 2008. The first integral method for solving some important nonlinear partial differential equations. Nonlinear Dynamics, 53(4), 281-286.
  9. Duran, S., 2021. Extractions of travelling wave solutions of (2+ 1)-dimensional Boiti–Leon–Pempinelli system via (Gʹ/G, 1/G)-expansion method. Optical and Quantum Electronics, 53(6), 1-12.
  10. Duran, S., Yokuş, A., and Durur, H., 2021. Surface wave behavior and refraction simulation on the ocean for the fractional Ostrovsky–Benjamin–Bona–Mahony equation. Modern Physics Letters B, 35(31), 2150477.
  11. Akgül, A., and Modanli, M., 2022. On Solutions of Fractional Telegraph Model With Mittag–Leffler Kernel. Journal of Computational and Nonlinear Dynamics, 17(2).
  12. Zayed, E. M. E., and Gepreel, K. A., 2009. The (G′/G)-expansion method for finding traveling wave solutions of nonlinear partial differential equations in mathematical physics. Journal of Mathematical Physics, 50(1), 013502.
  13. Yokuş, A., Durur, H., Duran, S., and Islam, M., 2022. Ample felicitous wave structures for fractional foam drainage equation modeling for fluid-flow mechanism. Computational and Applied Mathematics, 41(4), 1-13.
  14. Alam, M. N., Islam, S., İlhan, O. A., and Bulut, H., 2022. Some new results of nonlinear model arising in incompressible visco‐elastic Kelvin–Voigt fluid. Mathematical Methods in the Applied Sciences, 1–16.
  15. Ghanbari, B., 2021. New analytical solutions for the oskolkov-type equations in fluid dynamics via a modified methodology. Results in Physics, 28, 104610.
  16. Roshid, M. M., and Roshid, H. O., 2018. Exact and explicit traveling wave solutions to two nonlinear evolution equations which describe incompressible viscoelastic Kelvin-Voigt fluid. Heliyon, 4(8), e00756.
  17. Ak, T., Aydemir, T., Saha, A., and Kara, A. H., 2018. Propagation of nonlinear shock waves for the generalised Oskolkov equation and its dynamic motions in the presence of an external periodic perturbation. Pramana, 90(6), 1-16.