Magneto-Elektro-Elastik Çubuk Modelinin F Açılım Metodu ile Tam Çözümleri

Yıl 2021, , 375 - 392, 07.06.2021

Nisa Çelik

https://doi.org/10.17798/bitlisfen.873113

Öz

Bu çalışmada, dördüncü mertebeden lineer olmayan, magneto-elektro-elastik (MEE) çubuktaki yalnız gezen dalgalara karşılık gelen MEE kısmi diferensiyel denklemi ele alındı. Denklemin gezici dalga çözümlerini araştırmak için, F-açılım metodu kullanıldı. Metodun içerdiği farklı durumlar için Jacobi eliptik fonksiyonlar yardımı ile tam çözümler oluşturuldu. m→0 için trigonometrik, m→1 için hiperbolik fonksiyonlar ve bunların kombinasyonlarını içeren çözümler elde edildi. Son olarak çözümlerin farklı parametrelerdeki bazı özel değerleri için grafikleri Maple programı ile çizdirilerek incelenmeye sunulmuştur.

Anahtar Kelimeler

Lineer olmayan kısmi diferensiyel denklem, Magneto-Elektro-Elastik çubuk, F açılım Yöntemi, Jacobi eliptik fonksiyon

Kaynakça

• Yaşar E. 2016. Lie group analysis, exact solutions and conservation laws of (3+1) dimensional a B-type KP equation. NTMSCI 4, 4: 163-174.
• Yaşar E., Giresunlu İ.B. 2015. Lie symmetry reductions, exact solutions and conservation laws of the third order variant Boussinesq system. Acta Physica Polonica A, 128: 3.
• Yaşar E., Yıldırım Y. 2018. On the Lie symmetry analysis and travelling wave of time fractional fifth-order modified Sawada-Kotera equation. Karaelmas Fen ve Mühendislik Dergisi. 8 (2): 411-416.
• Liu H., Li J., Zhang Q. 2009. Lie symmetry analysis and exact explicit solutions for general Burger’s equation. Journal of Computational and Applied Mathematics, 228: 1-9.
• Giresunlu İ.B., Yaşar E. 2015. First integrals and exact solutions for path equation describing minimum drag work. Int. J. Adv. Appl. Math. And Mechi., 2 (4): 41-52.
• Akram G., Mahak N. 2018. Analytical solution of the Korteweg-de Vries equation and microtubule equation using the first integral method. Opt. Quantum Electorn, 50 (3): 145
• Wazwaz A.M. 2004. The tanh method for traveling wave solutions of nonlinear equations. Applied Mathematics and Computation, 154 (3): 713-723.
• Bekir A. 2008. Application of the (G'/G)-expansion method for nonlinear evolution equations. Physics Letter A, 372: 3400-3406.
• Liu S., Fu Z., Liu S., Zhao Q. 2001. Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equation. Physics Letter A, 289: 69-74.
• Mohyud-Din S.T., Ali A. 2017. -expansion Method and Shifted Chebyshev Wavelets for Generalized Sawada-Kotera of Fractional Order. Fundamental Informaticae, 151 (1-4): 173-190.
• He J.H., Wu X.H. 2006. Exp-function method for nonlinear wave equations. Chaos, Solitons &Fractals, 30 (3): 700-708.
• Zayed E.M.E., Alurrfi K.A.E. 2015. The modified Kudryashov method for solving someseventh order nonlinear PDEs in mathematical physics. World Journal of Modelling and Simulation, 11 (4): 308-319.
• Yıldırım Y., Çelik N., Yaşar E. 2017. Nonlinear Schrödinger equations with spatio-temporal dispersion in Kerr, parabolic, power and dual power law media: A novel extended Kudryashov’s algorithm and soliton solutions. Results in Physics, 7: 3116-3123.
• Ekici M., Sonmezoğlu A. 2019. Optical solitons with Biswas-Arshed equation by extended trial function method. Optik- International Journal for Light and Electron Optics, 177: 13-20.
• Dusunceli F., Celik E., Askin M., Bulut H. 2021. New exact solutions for the doubly dispersiveequation using the improved Bernoulli sub-equation function method. Indian J Phys., 95 (2): 309-314.
• Bulut H., Yel G., Başkonuş H. 2016. An application of Improved Bernoulli Sub-Equation Function Method to the Nonlinear Time Fractional Burgers Equation. Turk. J. Math. Comput. Sci., 5: 1-7.
• Mirhosseini-Alizamini S.M., Rezazadeh H., Srınıvasa K., Bekir A. 2020. New closed form solutions of the new coupled Konno-Oono equation using the new extendecd direct algebric method. Pramana-J. Phys., 94: 52.
• Xue C.X., Pan E., Zhang S.Y. 2011. Solitary waves in a magneto-elektro-elastic circular rod. Smart Mater. Struct., 20: 105010.
• Zhang T.T. 2019. On Lie symmetry analysis, conservation laws and solitary waves to a longitudinal wave motionequation. Applied Mathematics Letters, 98: 199-205.
• Baskonuş H.M., Bulut H., Atangana A. 2016. On the complex and hyperbolic structures of the longitudinal wave equation in a magneto-elektro-elastic rod. Smart Metar. Struct., 25: 035022.
• Zhou Q. 2016. Analytical study of solutions in magneto-elektro-elastic circular rod. Nonlinear Dyn, 83: 1403-1408.
• Darvishi M.T., Najafi M., Wazwaz A.M., 2020. Construction of exact solutions in a magnetoelectro-elastic circular rod. Waves in Random and Complex Media, 30 (2): 340-353.
• Iqbal M., Seadawy A.R., Lu D. 2019. Applications of nonlinear longitudinal wave equation in a magneto-electro-elastic circular rod and new solitary wave solutions. Modern Physics Letters B, 33 (18): 1950210.
• Seadawy A.R., Manafian J. 2018. New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod. Results in Physics, 8: 1158-1167.
• Zhou Y., Wang M., Wang Y. 2003. Periodic wave solutions to a coupled KdV equations with variable coefficient. Physics Letters A, 308: 31-36.
• Zhang J.F., Dai C.Q., Yang Q., Zhu J.M. 2005. Variable-coefficient F-expansion method and its application to nonlinear Schrödinger equation. Optics Communications, 252: 408-442.
• Zhang J.L., Wang M.L., Wang Y.M., Fang Z.D. 2006. The Improved F expansion method and its applications. Physics Letter A, 350: 103-109.
• Ebaid A., Aly E.H. 2012. Exact solutions for the transformed reduced Ostrovsky equation via the F-expansion method in terms of Weierstrass-elliptic and Jacobian-elliptic functions. Wave Motion, 49: 296-308.
• Zhao Y.M. 2013. F-Expansion Method and Its Application for Finding New Exact Solutions to the Kudryashov-Sinelshchikov Equation. Journal of Applied Mathematics, Volume 2013, Article ID 895760, 7 pages, doi: 10.1155/2013/895760
• Çelik N., Seadawy A.R., Sağlam Y., Yaşar E. 2021. A model of solitary waves in a nonlinear elastic circular rod: Abundant different type exact solutions and conservation laws. Choas, Solitons and Fractals, 143: 1-19.