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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 the Special Issue: Analytical Methods for Nonlinear Vibration & Active Control in Nano/Micro Devices and Systems)

Sound & Vibration 2021, 55(3), 241-251. https://doi.org/10.32604/sv.2021.014157

## Abstract

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.

## Keywords

APA Style
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. https://doi.org/10.32604/sv.2021.014157
Vancouver Style
Durur H, Yokuş A, Kaya D, Ahmad H. Modeling of dark solitons for nonlinear longitudinal wave equation in a magneto-electro-elastic circular rod. Sound Vib . 2021;55(3):241-251 https://doi.org/10.32604/sv.2021.014157
IEEE Style
H. Durur, A. Yokuş, D. Kaya, and H. Ahmad "Modeling of Dark Solitons for Nonlinear Longitudinal Wave Equation in a Magneto-Electro-Elastic Circular Rod," Sound Vib. , vol. 55, no. 3, pp. 241-251. 2021. https://doi.org/10.32604/sv.2021.014157

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