Research Article

Cubic–quartic optical soliton perturbation and modulation instability analysis in polarization-controlled fibers for Fokas–Lenells equation

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 123, Muscat, Oman
³ Department of Mathematics and Physics, Grambling State University, Grambling, LA 71245, USA
⁴ Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
⁵ Department of Applied Mathematics, National Research Nuclear University, 31 Kashirskoe Hwy, Moscow 115409, Russian Federation
⁶ Department of Applied Sciences, Cross-Border Faculty, Dunarea de Jos University of Galati, 111 Domneasca Street, Galati 800201, Romania
⁷ Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa 0204, Pretoria, South Africa

^* Corresponding author: khalil.ibr@cas.edu.om

Received: 20 January 2022
Accepted: 28 July 2022

Abstract

The objective of this study is to investigate miscellaneous wave structures for perturbed Fokas–Lenells equation (FLE) with cubic-quartic dispersion in polarization-preserving fibers. Based on the improved projective Riccati equations method, various types of soliton solutions such as bright soliton, combo dark–bright soliton, singular soliton and combo singular soliton are constructed. Additionally, a set of periodic singular waves are also retrieved. The dynamical behaviors of some obtained solutions are depicted to provide a key to understanding the physics of the model. The modulation instability of the FLE is reported by employing the linear stability analysis which shows that all solutions are stable.