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

Year 2021, Volume: 10 Issue: 2, 375 - 392, 07.06.2021
https://doi.org/10.17798/bitlisfen.873113

Abstract

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.

References

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  • 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.
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  • 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.
Year 2021, Volume: 10 Issue: 2, 375 - 392, 07.06.2021
https://doi.org/10.17798/bitlisfen.873113

Abstract

References

  • 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.
There are 30 citations in total.

Details

Primary Language Turkish
Journal Section Araştırma Makalesi
Authors

Nisa Çelik 0000-0003-1209-991X

Publication Date June 7, 2021
Submission Date February 2, 2021
Acceptance Date April 18, 2021
Published in Issue Year 2021 Volume: 10 Issue: 2

Cite

IEEE N. Çelik, “Magneto-Elektro-Elastik Çubuk Modelinin F Açılım Metodu ile Tam Çözümleri”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 10, no. 2, pp. 375–392, 2021, doi: 10.17798/bitlisfen.873113.

Bitlis Eren University
Journal of Science Editor
Bitlis Eren University Graduate Institute
Bes Minare Mah. Ahmet Eren Bulvari, Merkez Kampus, 13000 BITLIS