On the new wave behavior of the Magneto-Electro-Elastic(MEE) circular rod longitudinal wave equation

Onur Alp İlhan; Hasan Bulut; Tukur Abdulkadir Sulaiman; Haci Mehmet Baskonus

doi:10.11121/ijocta.01.2020.00837

Authors

Onur Alp İlhan Erciyes Üniversitesi Eğitim Fakültesi İlköğretim Matematik http://orcid.org/0000-0003-1618-6439
Hasan Bulut Firat Üniversitesi Fen Edebiyat Fakültesi, Matematik Bölümü-Elazığ http://orcid.org/0000-0002-6089-1517
Tukur Abdulkadir Sulaiman Firat Üniversitesi Fen Edebiyat Fakültesi, Matematik Bölümü-Elazığ http://orcid.org/0000-0001-7284-8332
Haci Mehmet Baskonus Harran University Eğitim Fakültesi Şanlıurfa http://orcid.org/0000-0003-4085-3625

DOI:

https://doi.org/10.11121/ijocta.01.2020.00837

Keywords:

The SGEM, longitudinal wave equation in a MEE circular rod, complex, hyperbolic, trigonometric function solutions.

Abstract

The analytical solution of the longitudinal wave equation in the MEE circular rod is analyzed by the powerful sine-Gordon expansion method. Sine - Gordon expansion is based on the well-known wave transformation and sine - Gordon equation. In the longitudinal wave equation in mathematical physics, the transverse Poisson MEE circular rod is caused by the dispersion. Some solutions with complex, hyperbolic and trigonometric functions have been successfully implemented. Numerical simulations of all solutions are given by selecting the appropriate parameter values. The physical meaning of the analytical solution explaining some practical physical problems is given.

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Author Biographies

Onur Alp İlhan, Erciyes Üniversitesi Eğitim Fakültesi İlköğretim Matematik

Onur Alp ilhan received his Master’s Degree (2002) in Mathematics from Erciyes University and obtained a PhD Degree (2005) from National University of Uzbekistan. Mr. İlhan is currently working as an Associate Professor at Faculty of Education in Erciyes University,. His research interests include Mathbio. ODE, PDE and Integral equations.

Hasan Bulut, Firat Üniversitesi Fen Edebiyat Fakültesi, Matematik Bölümü-Elazığ

Hasan Bulut is currently professor of Mathematics in Firat University. His research interests include stochastic differential equations, fluid and heat mechanics, finite element method, analytical methods for nonlinear differential equations and numerical solutions of the partial differential equations.

Tukur Abdulkadir Sulaiman, Firat Üniversitesi Fen Edebiyat Fakültesi, Matematik Bölümü-Elazığ

Tukur Abdulkadir Sulaiman is a research assistant at Firat University, Turkey and an assistant lecturer as Federal University Dutse, Nigeria. He is currently pursuing his PhD. (Applied Mathematics) in Firat University, Turkey. He has so far published 4 articles in various journals. His research interests include; stochastic optimization, analytical and numerical solutions of nonlinear ordinary/partial differential equations including the fractional differential equations.

Haci Mehmet Baskonus, Harran University Eğitim Fakültesi Şanlıurfa

Haci Mehmet Baskonus received the PhD degree in Mathematics from the Firat University, Turkey, in 2014. He is currently an Assoc. Prof. Dr at Faculty of Education in Harran University. His research interests include ordinary and partial differential equations, analytical methods for linear and nonlinear differential equations, mathematical physics, numerical solutions of the partial differential equations, fractional differential equations (of course ordinary and partial) and computer programming like Mathematica.

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