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Modeling of Dark Solitons for Nonlinear Longitudinal Wave Equation in a Magneto-Electro-Elastic Circular Rod

Hulya Durur1, Asıf Yokuş2, Doğan Kaya3, Hijaz Ahmad4,*
1 Department of Computer Engineering, Faculty of Engineering, Ardahan University, Ardahan, Turkey
2 Department of Mathematics, Faculty of Science, Firat University, Elazig, Turkey
3 Department of Mathematics, Istanbul Commerce University, Istanbul, Turkey
4 Department of Basic Sciences, University of Engineering and Technology, Peshawar, Pakistan
* Corresponding Author: Hijaz Ahmad. Email:
(This article belongs to this Special Issue: Analytical Methods for Nonlinear Vibration & Active Control in Nano/Micro Devices and Systems)

Sound & Vibration 2021, 55(3), 241-251.

Received 03 September 2020; Accepted 28 September 2020; Issue published 15 July 2021


In this paper, sub equation and expansion methods are proposed to construct exact solutions of a nonlinear longitudinal wave equation (LWE) in a magneto-electro-elastic circular rod. The proposed methods have been used to construct hyperbolic, rational, dark soliton and trigonometric solutions of the LWE in the magneto-electro-elastic circular rod. Arbitrary values are given to the parameters in the solutions obtained. 3D, 2D and contour graphs are presented with the help of a computer package program. Solutions attained by symbolic calculations revealed that these methods are effective, reliable and simple mathematical tool for finding solutions of nonlinear evolution equations arising in physics and nonlinear dynamics.


(1/G’)-expansion method; sub equation method; exact solution; traveling wave solution; nonlinear evolution equations

Cite This Article

Durur, H., Yokuş, A., Kaya, D., Ahmad, H. (2021). Modeling of Dark Solitons for Nonlinear Longitudinal Wave Equation in a Magneto-Electro-Elastic Circular Rod. Sound & Vibration, 55(3), 241–251.


This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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