$ M- $truncated optical soliton and their characteristics to a nonlinear equation governing the certain instabilities of modulated wave trains

Abdullahi Yusuf; Tukur A. Sulaiman; Mustafa Inc; Sayed Abdel-Khalek; K. H. Mahmoud; Abdullahi Yusuf; Tukur A. Sulaiman; Mustafa Inc; Sayed Abdel-Khalek; K. H. Mahmoud

doi:10.3934/math.2021535

AIMS Mathematics

2021, Volume 6, Issue 9: 9207-9221. doi: 10.3934/math.2021535

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$ M- $truncated optical soliton and their characteristics to a nonlinear equation governing the certain instabilities of modulated wave trains

1.
Department of Computer Engineering, Biruni University, Istanbul, Turkey
2.
Department of Mathematics, Federal University Dutse, Jigawa, Nigeria
3.
Department of Mathematics, Science Faculty, Firat University Elazig, Turkey
4.
Department of Medical Research, China Medical University Hospital, China Medical University, 40402 Taichung, Taiwan
5.
Department of Mathematics, College of Science, P.O. Box 11099, Taif University, Taif 21944, Saudi Arabia
6.
Department of Physics, College of Khurma University College, Taif University, P.O. Box11099, Taif 21944, Saudi Arabia

Received: 11 December 2020 Accepted: 20 May 2021 Published: 21 June 2021
MSC : 35A09, 35E05

This study investigates the nonlinear Hamiltonian amplitude equation by using two analytical techniques, namely; the extended sinh-Gordon equation expansion method, and the extended rational sine-cosine/sinh-cosh methods. Some important wave solutions are successfully constructed, such as dark, bright, combined dark-bright, singular solitons, periodic and singular periodic wave solutions. The physical features of the acquired solutions are plotted to depict the clear dynamical behaviour of the reported results. All the acquired solutions have satisfied the original equation.
- Hamiltonian amplitude equation,
- extended sinh-Gordon method,
- extended rational sine-cosine/sinh-cosh,
- optical solitons,
- M-truncated derivative
Citation: Abdullahi Yusuf, Tukur A. Sulaiman, Mustafa Inc, Sayed Abdel-Khalek, K. H. Mahmoud. $ M- $truncated optical soliton and their characteristics to a nonlinear equation governing the certain instabilities of modulated wave trains[J]. AIMS Mathematics, 2021, 6(9): 9207-9221. doi: 10.3934/math.2021535

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Abstract

This study investigates the nonlinear Hamiltonian amplitude equation by using two analytical techniques, namely; the extended sinh-Gordon equation expansion method, and the extended rational sine-cosine/sinh-cosh methods. Some important wave solutions are successfully constructed, such as dark, bright, combined dark-bright, singular solitons, periodic and singular periodic wave solutions. The physical features of the acquired solutions are plotted to depict the clear dynamical behaviour of the reported results. All the acquired solutions have satisfied the original equation.

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