# Implicit Quiescent Optical Solitons for the Dispersive Concatenation Model with Nonlinear Chromatic Dispersion by Lie Symmetry

## Authors

• Abdullahi Rashid Adem Department of Mathematical Sciences, University of South Africa, South Africa
• Anjan Biswas Department of Mathematics and Physics, Grambling State University, Grambling, LA, USA
• Yakup Yildirim Department of Computer Engineering, Biruni University, Istanbul, Turkey
• Asim Asiri Mathematical Modeling and Applied Computation Research Group, Center of Modern Mathematical Sciences and their Applications, Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

## Keywords:

solitons, quiescent, dispersive, Lie transform

## Abstract

The primary purpose of this paper is to investigate and recover implicit quiescent optical solitons in the context of the dispersive concatenation model in nonlinear optics. Specifically, the study focuses on a model that incorporates nonlinear chromatic dispersion and includes Kerr and power-law self-phase modulation effects. The objective is to identify and characterize these soliton solutions within this complex optical system. To achieve this purpose, we employ the Lie symmetry analysis method. Lie symmetry analysis is a powerful mathematical technique commonly used in physics and engineering to identify symmetries and invariance properties of differential equations. In this context, it is used to uncover the underlying symmetries of the nonlinear optical model, which in turn aids in the recovery of the quiescent optical solitons. This method involves mathematical derivations and calculations to determine the solutions. The outcomes of the current paper include the successful recovery of implicit quiescent optical solitons for the dispersive concatenation model with nonlinear chromatic dispersion, Kerr, and power-law self-phase modulation. The study provides mathematical expressions and constraints on the model’s parameters that yield upper and lower bounds for these solutions. Essentially, this paper presents a set of mathematical descriptions for the optical solitons that can exist within the described optical system. The present paper contributes to the field of nonlinear optics by exploring the behavior of optical solitons in a model that combines multiple nonlinear effects. This extends our understanding of complex optical systems.

2023-10-09

## How to Cite

1.
Adem AR, Biswas A, Yildirim Y, Asiri A. Implicit Quiescent Optical Solitons for the Dispersive Concatenation Model with Nonlinear Chromatic Dispersion by Lie Symmetry. Contemp. Math. [Internet]. 2023 Oct. 9 [cited 2024 May 28];4(4):666-74. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/3575

Research Article

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