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

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.


Keywords


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

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Ren, Y.J., Liu S.T., and Zhang, H.Q. (2007). A new generalized algebra method and its application in the (2+1)-dimensional Boiti-Leon-Pempinelli equation. Chaos Solitons and Fractals, 32, 1655-1665.

Manafian, J. (2016). Optical soliton solutions for Schr¨odinger type nonlinear evolution equations by the tan(F()/2)-expansion method. Optik-International Journal of Light and Electron Optics, 127, 4222-4245.

Feng, W.G., Li, K.M., Li, Y.Z. and Lin, C. (2009). Explicit exact solutions for (2+1)- dimensional Boiti-Leon-Pempinelli equation. Communications in Non-linear Science and Numerical Simulation, 14, 2013-2017.

Fu, Z., Liu, S. and Zhao, Q. (2001) New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations. Physics Letters A, 290, 72-76.

Zayed, E.M.E. and Alurrfi, K.A.E. (2014). The homogeneous balance method and its applications for finding the exact solutions for nonlinear evolution equations. Italian Journal of Pure and Applied Mathematics, 33, 307-318.

Islam, M.S, Khan, K. and Arnous, A.H. (2015). Generalized Kudryashov method for solving some (3+1)-dimensional nonlinear evolution equations. New Trends in Mathematical Sciences, 3(3), 46-57.

Lu, H.L., Liu, X.Q. and Niu, L. (2010). A generalized (G'/G)-expansion method and its applications to nonlinear evolution equations. Applied Mathematics and Computation, 215, 3811-3816.

Wang, C. (2016). Dynamic behavior of traveling waves for the Sharma-Tasso-Olver equation. Non-linear Dynamics, 85(2), 1119-1126.

Baskonus, H.M. and Bulut, H. (2016). Exponential prototype structures for (2+1)- dimensiona Boiti-Leon-Pempinelli systems in mathematical physics. Waves in Random and Complex Media, 26(2), 201-208.

Baskonus, H.M., Bulut, H. and Belgacem, F.B.M. (2017). Analytical Solutions for nonlinear long-short wave interaction systems with highly complex structure. Journal of Computational and Applied Mathematics, 312, 257-266.

Kadkhoda, N. and Jafari, H. (2016). Kudryashov method for exact solutions of isothermal magnetostatic atmospheres. Applied Mathematics and Computation, 6(1), 43-52.

El-wakil, S.A., El-labany, S.K., Zahran, M.A. and Sabry, R. (2002). Modified extended tanh-function method for solving nonlinear partial differential equations. Physics Letters A, 299, 179-188.

Islam, M.S., Khan, K., Arnous, A.H. (2015). Generalized Kudryashov method for solving some (3+1)-dimensional nonlinear evolution equations. New Trends in Mathematical Sciences, 3(3), 46-57.

Chen, H.T., Hong-Qing, Z. (2004). New double periodic and multiple soliton solutions of the generalized (2 + 1)-dimensional Boussinesq equation. Chaos Solitons and Fractals, 20, 765-769.

Baskonus, H.M. and Bulut, H. (2015). On some new analytical solutions for The (2+1)- dimensional burgers equation and the special type of Dodd- Bullough-Mikhailov equation. Journal of Applied Analysis and Computation, 5(4), 613-625.

Lu, Z. and Zhang, H. (2004). Soliton like and multi-soliton like solutions for the Boiti- Leon-Pempinelli equation. Chaos, Solitons and Fractals, 19, 527-531.

Huang, D.J. and Zhang, H.Q. (2004). Exact Travelling Wave Solutions for the Boiti-Leon-Pempinelli Equation. Chaos Solitons and Fractals, 22, 243-247.

Dai, C. and Wang, Y. (2009). Periodic Structures Based on Variable Separation Solution of the (2+1)-Dimensional Boiti-Leon-Pempinelli Equation. Chaos Solitons and Fractals, 39, 350-355.

Liang, Y. (2014). Exact solutions of the (3+1)-dimensional modified KdV- Zakharov-Kuznetsev equation and Fisher equations using the modified simple equation method. Journal of Interdisciplinary Mathematics, 17, 565-578.

Zhang, H. (2007). Extended jacobi elliptic function expansion method and its applications. Communications in Non-linear Science and Numerical Simulation, 12(5), 627-635.

Petrovic, N.Z. and Bohra, M. (2016). General jacobi elliptic function expansion method applied to the generalized (3 + 1)-dimensional nonlinear Schrodinger equation. Optical and Quantum Electronics, 48, (268).

Yan, Z. (2003). Jacobi elliptic function solutions of nonlinear wave equations via the new sinh-gordon equation expansion method. MM Research Preprints, 22, 363-375.

Manafian, J. and Lakestani, M. (2019). Lump-type solutions and interaction phenomenon to the bidirectional Sawada- Kotera equation. Pramana, 92:41.

Manafian, J. (2018). Novel solitary wave solutions for the (3+1)-dimensional extended Jimbo-Miwa equations. Computers & Mathematics with Applications, 76(5), 1246-1260.

Manafian, J., Mohammadi-Ivatloo, B. and Abapour, M. (2019). Lump-type solutions and interaction phenomenon to the (2+1)-dimensional breaking soliton equation. Applied Mathematics and Computation Volume, 356, 13-41.

Ilhan, O.A., Manafian, J. and Shahriari M. (2019). Lump wave solutions and the interaction phenomenon for a variable coefficient Kadomtsev-Petviashvili equation. Computers & Mathematics with Applications, In press.

Foroutan, M., Manafian, J. and Ranjbaran, A. (2018). Lump solution and its interaction to (3+1)-D potential-YTSF equation. Nonlinear Dynamics, 92, 2077-2092.

Mohammad, S. and Manafian, J. (2019). Analytical behaviour of lump solution and interaction phenomenon to the Kadomtsev-Petviashvili-like equation. Pramana, 93:3.

Seadawy, A.R. and Manafian, J. (2018). New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod. Results in Physics, 8, 1158-1167.

Ramin, M.T., Manafian, J., Baskonus, H.M. and Dusunceli, F. (2019). Applications of He’s semi-inverse variational method and ITEM to the nonlinear long-short wave interaction system, IJAAS Journal, 6(8), 53-64.

Yan, C. (1996). A simple transformation for nonlinear waves. Physics Letters A , 22(4), 77-84.

Bulut, H., Sulaiman, T.A. and Baskonus, H.M. (2016). New solitary and optical wave structures to the Korteweg-de Vries equation with dual-power law nonlinearity. Optical and Quantum Electronics, 48:564, 1-14.

Baskonus, H.M., Bulut, H. and Atangana, A. (2016). On the complex and hyperbolic structures of longitudinal wave equation in a Magneto-Electro-Elastic circular rod. Smart Materials and Structures, 25(3), 035022.

Xue, C.X., Pan, E. and Zhang, X.Y. (2011). Solitary waves in a Magneto-Electro-Elastic circular rod. Smart Materials and Structures, 20(10), 035022.

Ma, X., Pan, Y. and Chang, L. (2013). Explicit travelling wave solutions in a Magneto-Electro-Elastic circular rod. International Journal of Computer Science Issues, 10(1), 62-68.

Khan, K., Koppelaar, H. and Akbar, A. (2016). Exact and numerical soliton solutions to nonlinear wave equations. Computational and Mathematical Engineering, 2, 5-22.

Younis, M. and Ali, S. (2015). Dark and singular solitons in Magneto-Electro-Elastic circular rod. Waves in Random and Complex Media, 25(4), 549-555.

Yan, Z. and Zhang, H. (1999). New explicit and exact travelling wave solutions for a system of variant Boussinesq equations in mathematical physics. Physics Letters A, 252, 291-296

Zhen-Ya, Y., Hong-oing, Z. and En-Gui, F. (1999). New explicit and travelling wave solutions for a class of nonlinear evolution equations. Acta Physica Sinica, 48(1), 1-5.

Weisstein, E.W. (2002). Concise encyclope- dia of nathematics. 2nd edition (New York: CRC Press).




DOI: http://dx.doi.org/10.11121/ijocta.01.2020.00837

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