Research Article

Chirped gap solitons with Kudryashov’s law of self-phase modulation having dispersive reflectivity

¹ University of Technology and Applied Sciences, P.O. Box 14, Ibri 516, Oman
² Department of Mathematics, Sultan Qaboos University, P.O. Box 36, Al-Khod, Muscat 123, Oman
³ Department of Mathematics and Physics, Grambling State University, Grambling, LA-71245, USA
⁴ 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
⁵ Department of Applied Sciences, Cross-Border Faculty of Humanities, Economics and Engineering, Dunarea de Jos University of Galati, 111 Domneasca Street, 800201 Galati, Romania
⁶ Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa-0204, Pretoria, South Africa

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

Received: 14 August 2023
Accepted: 12 September 2023

Abstract

The present study is devoted to investigate the chirped gap solitons with Kudryashov’s law of self-phase modulation having dispersive reflectivity. Thus, the mathematical model consists of coupled nonlinear Schrödinger equation (NLSE) that describes pulse propagation in a medium of fiber Bragg gratings (BGs). To reach an integrable form for this intricate model, the phase-matching condition is applied to derive equivalent equations that are handled analytically. By means of auxiliary equation method which possesses Jacobi elliptic function (JEF) solutions, various forms of soliton solutions are extracted when the modulus of JEF approaches 1. The generated chirped gap solitons have different types of structures such as bright, dark, singular, W-shaped, kink, anti-kink and Kink-dark solitons. Further to this, two soliton waves namely chirped bright quasi-soliton and chirped dark quasi-soliton are also created. The dynamic behaviors of chirped gap solitons are illustrated in addition to their corresponding chirp. It is noticed that self-phase modulation and dispersive reflectivity have remarkable influences on the pulse propagation. These detailed results may enhance the engineering applications related to the field of fiber BGs.