Research Article

Sub-pico-second chirped optical solitons in birefringent fibers for space–time fractional Kaup-Newell equation

¹ Mathematics and Computing Skills Unit, University of Technology and Applied Sciences, PO Box 466, Ibri 516, Oman
² Department of Mathematics and Physics, Grambling State University, Grambling, LA 71245-2715, USA
³ Mathematical Modeling and Applied Computation (MMAC) Research Group, Center of Modern Mathematical Sciences and their Applications (CMMSA), Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
⁴ Department of Applied Sciences, Cross-Border Faculty of Humanities, Economics and Engineering, Dunarea de Jos University of Galati, 111 Domneasca Street, 800201 Galati, Romania
⁵ Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa 0204, Pretoria, South Africa
⁶ Department of Computer Engineering, Biruni University, Istanbul, 34010, Turkey
⁷ Department of Mathematics, Near East University, 99138, Nicosia, Cyprus

^* Corresponding author: khalil.alghafri@utas.edu.om

Received: 3 November 2024
Accepted: 21 January 2025

Abstract

The present work is devoted to investigate the chirped bright and dark optical solitons of fractional Kaup-Newell equation (KNE) in birefringent fibers. The study is carried out analytically by the traveling wave hypothesis with the conformable derivative which reduces the governing model to an ordinary differential equation (ODE). The obtained equation is handled with the aid of an exotic integration scheme that utilizes the Jacobi elliptic equation in the form of a first-order nonlinear ODE with three-degree terms. Taking the modulus of Jacobi elliptic function to unity, distinct types of bright and dark optical solitons are derived with their corresponding chirping. The fractional order derivative is noted to have a significant influence on the pulse propagation. Additionally, the nonlinearity amount causes also marked variations in the amplitude and width of solitons. The modulation instability of the KNE is reported by implementing the linear stability analysis which confirms that all solutions are stable. The revealed results can be capitalized in improving the relevant physical and engineering applications in the field of birefringent fiber.