Exact Solutions of the Oskolkov Equation in Fluid Dynamics

Year 2023, Volume: 23 Issue: 2, 355 - 361, 03.05.2023

Hülya Durur

https://doi.org/10.35414/akufemubid.1119363

Cited By: 1

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).

Keywords

Sub equation method;, Oskolkov equation;, Nonlinear partial differential equation;, Exact solution

Akışkanlar Dinamiğinde Oskolkov Denkleminin Tam Çözümleri

Abstract

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.

Keywords

Alt denklem metodu;, Oskolkov denklemi;, Lineer olmayan kısmi diferansiyel denklem;, Tam çözüm

References

• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• Raslan, K. R., 2008. The first integral method for solving some important nonlinear partial differential equations. Nonlinear Dynamics, 53(4), 281-286.
• 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.
• 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.
• Akgül, A., and Modanli, M., 2022. On Solutions of Fractional Telegraph Model With Mittag–Leffler Kernel. Journal of Computational and Nonlinear Dynamics, 17(2).
• 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.
• 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.
• 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.
• Ghanbari, B., 2021. New analytical solutions for the oskolkov-type equations in fluid dynamics via a modified methodology. Results in Physics, 28, 104610.
• 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.
• 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.