Sıkıştırılamaz Visko Elastik Kelvin-Voigt Sıvısında Ortaya Çıkan Oskolkov Denkleminin Gezici Dalga Çözümleri

Bu çalışmada, sıkıştırılamaz visko-elastik Kelvin-Voigt akışkanının dinamiklerini tanımlayan Oskolkov denkleminin tam çözümleri sunulmuştur. Bu çözümleri aramak için -açılım yöntemi kullanılmaktadır. Elde edilen tam çözümlerinin dinamikleri uygun parametreler yardımıyla analiz edilmiş ve grafiklerle sunulmuştur. Uygulanan yöntem, mühendislik alanlarında görülen çeşitli dinamik modelleri zenginleştiren temel doğrusal olmayan dalgaları aramak için etkili ve güvenilirdir. Oskolkov denkleminin çalşmasında kullanılan analitik metodun gezici dalga çözümlerini ortaya koymakta güvenilir, geçerli ve faydalı bir araç olduğu sonucu elde edilir.

Anahtar Kelimeler:

Oskolkov denklemi, açılım yöntemi, gezici dalga çözümü, tam çözüm

Traveling Wave Solutions of the Oskolkov Equation Arising in Incompressible Viscoelastic Kelvin–Voigt Fluid

In this manuscript, exact solutions of the Oskolkov equation, which describes the dynamics of incompressible viscoelastic Kelvin-Voigt fluid, are presented. The -expansion method is used to search for these solutions. The dynamics of the obtained exact solutions are analyzed with the help of appropriate parameters and presented with graphics. The applied method is efficient and reliable to search for fundamental nonlinear waves that enrich the various dynamical models seen in engineering fields. It is concluded that the analytical method used in the study of the Oskolkov equation is reliable, valid and useful tool for created traveling wave solutions.

Keywords:

Oskolkov equation, expansion method, traveling wave solution, exact solution,

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Alam, M. N., Islam, S., İlhan, O. A., & Bulut, H. (2022). Some new results of nonlinear model arising in incompressible visco‐elastic Kelvin–Voigt fluid. Mathematical Methods in the Applied Sciences. DOI: 10.1002/mma.8372
Roshid, M., & Bashar, H. (2019). Breather wave and kinky periodic wave solutions of one-dimensional Oskolkov equation. Mathematical Modelling of Engineering Problems, 6(3), 460-466.
Wazwaz, A. M. (2004). The tanh method for traveling wave solutions of nonlinear equations. Applied Mathematics and Computation, 154(3), 713-723.
Darvishi, M., Arbabi, S., Najafi, M. & Wazwaz, A. (2016). Traveling Wave Solutions of a (2+ 1)-Dimensional Zakharov-Like Equation by the First Integral Method and the Tanh Method. Optik, 127(16), 6312-6321.
Tripathy, A., Sahoo, S., Rezazadeh, H., & Izgi, Z. P. (2022). New optical analytical solutions to the full nonlinearity form of the space–time Fokas–Lenells model of fractional-order. International Journal of Modern Physics B, 2250058.
Karakoc, S. B. G., & Ali, K. K. (2021). Theoretical and computational structures on solitary wave solutions of Benjamin Bona Mahony-Burgers equation. Tbilisi Mathematical Journal, 14(2), 33-50.
Yokuş, A., Durur, H., Duran, S., & 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.
Duran, S., & Karabulut, B. (2022). Nematicons in liquid crystals with Kerr Law by sub-equation method. Alexandria Engineering Journal, 61(2), 1695-1700.
Yokuş, A., Duran, S., & Durur, H. (2022). Analysis of wave structures for the coupled Higgs equation modelling in the nuclear structure of an atom. The European Physical Journal Plus, 137(9), 1-17.
Durur, H., Tasbozan, O., & Kurt, A. (2020). New analytical solutions of conformable time fractional bad and good modified Boussinesq equations. Applied Mathematics and Nonlinear Sciences, 5(1), 447-454.
Karakoc, S. B. G., & Ali, K. K. (2021). New exact solutions and numerical approximations of the generalized kdv equation. Computational Methods for Differential Equations, 9(3), 670–691.
Isah, M. A., & Yokuş, A. (2022). The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity. Mathematical Modelling and Numerical Simulation with Applications, 2(3), 147-163.
Yokus, A., & Isah, M. A. (2022). Stability analysis and solutions of (2+ 1)-Kadomtsev–Petviashvili equation by homoclinic technique based on Hirota bilinear form. Nonlinear Dynamics, 1-12.
Özkan, Y. S., Seadawy, A. R., & Yaşar, E. (2021). On the optical solitons and local conservation laws of Chen–Lee–Liu dynamical wave equation. Optik, 227, 165392.
Yavuz, M., & Yokus, A. (2020). Analytical and numerical approaches to nerve impulse model of fractional‐order. Numerical Methods for Partial Differential Equations, 36(6), 1348-1368.
Ali, K. K., Karakoc, S. B. G., & Rezazadeh, H. (2020). Optical soliton solutions of the fractional perturbed nonlinear schrodinger equation. TWMS Journal of Applied and Engineering Mathematics, 10(4), 930-939.
Baskonus, H. M. (2021). Dark and trigonometric soliton solutions in asymmetrical Nizhnik-Novikov-Veselov equation with (2+ 1)-dimensional. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 11(1), 92-99.
Veeresha, P., Yavuz, M., & Baishya, C. (2021). A computational approach for shallow water forced Korteweg–De Vries equation on critical flow over a hole with three fractional operators. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 11(3), 52-67.
Yavuz, M., & Abdeljawad, T. (2020). Nonlinear regularized long-wave models with a new integral transformation applied to the fractional derivative with power and Mittag-Leffler kernel. Advances in Difference Equations, 2020(1), 1-18.
Karakoc, S. B. G., Bhowmik, S. K., & Sucu, D. Y. (2021). A Novel Scheme Based on Collocation Finite Element Method to GeneralisedOskolkov Equation. Journal of Science and Arts, 21(4), 895-908.
Yokuş, A., Durur, H., & 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.
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., & 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.
Thabet, H., Kendre, S., & Peters, J. (2022). Advances in solving conformable nonlinear partial differential equations and new exact wave solutions for Oskolkov‐type equations. Mathematical Methods in the Applied Sciences, 45(5), 2658-2673.
Gözükızıl, Ö. F., & Akçağıl, Ş. (2013). The tanh-coth method for some nonlinear pseudoparabolic equations with exact solutions. Advances in Difference Equations, 1, 1-18.
Duran, S. (2021). Travelling wave solutions and simulation of the Lonngren wave equation for tunnel diode. Optical and Quantum Electronics, 53(8), 1-9.
Yokus, A. (2011). Solutions of some nonlinear partial differential equations and comparison of their solutions, Ph.Diss., Fırat University.