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ARTICLE

Bifurcation Analysis and Bounded Optical Soliton Solutions of the Biswas-Arshed Model

Fahad Sameer Alshammari¹, Md Fazlul Hoque², Harun-Or-Roshid², Muhammad Nadeem^3,*
1 Department of Mathematics, College of Science at Alkharj, Prince Sattam bin Abdulaziz University, Alkharj, 11942, Saudi Arabia
2 Department of Mathematics, Pabna University of Science and Technology, Pabna, 6600, Bangladesh
3 Faculty of Science, Yibin University, Yibin, 644000, China
* Corresponding Author: Muhammad Nadeem. Email:
(This article belongs to this Special Issue: Fractal-Fractional Models for Engineering & Sciences)

Computer Modeling in Engineering & Sciences 2023, 135(3), 2197-2217. https://doi.org/10.32604/cmes.2023.022301

Received 03 March 2022; Accepted 19 April 2022; Issue published 23 November 2022

Abstract

We investigate the bounded travelling wave solutions of the Biswas-Arshed model (BAM) including the low group velocity dispersion and excluding the self-phase modulation. We integrate the nonlinear structure of the model to obtain bounded optical solitons which pass through the optical fibers in the non-Kerr media. The bifurcation technique of the dynamical system is used to achieve the parameter bifurcation sets and split the parameter space into various areas which correspond to different phase portraits. All bounded optical solitons and bounded periodic wave solutions are identified and derived conforming to each region of these phase portraits. We also apply the extended sinh-Gordon equation expansion and the generalized Kudryashov integral schemes to obtain additional bounded optical soliton solutions of the BAM nonlinearity. We present more bounded optical shock waves, the bright-dark solitary wave, and optical rogue waves for the structure model via these schemes in different aspects.

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Keywords

The Biswas-Arshed model; the extended sinh-Gordon equation expansion; the generalized Kudryashov approach; shock wave double solitons; optical singular double solitons; chirp-free bright-dark double solitons

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