Eur. Phys. J. Plus (2020) 135: 371
https://doi.org/10.1140/epjp/s13360-020-00382-z

Regular Article

Propagation of W-shaped, M-shaped and other exotic optical solitons in the perturbed Fokas–Lenells equation

¹ Department of Physics, Faculty of Science, University of Maroua, P.O. Box 814, Maroua, Cameroon
² Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaoundé, Cameroon
³ Faculty of science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
⁴ Higher Teachers’ Training College of Maroua, University of Maroua, P.O. Box 55, Maroua, Cameroon
⁵ Department of Physics, Faculty of Science, University of Ngaoundere, P.O. Box 454, Ngaoundere, Cameroon

^* e-mail: malwehubert@yahoo.fr

Received: 9 December 2019
Accepted: 3 April 2020
Published online: 24 April 2020

Abstract

This work investigates the perturbed Fokas–Lenells equation form which describes the propagation of ultrashort pulses in optical fibers. Based on the complex envelope ansatz method, the study reveals that waves which propagate in this medium are solitary waves type precisely M-shaped and W-shaped solitons. The study of wave propagation and their robustness that are analytically obtained are aligned to numerical study. The profiles have been perturbed with 1% noise level. From this, it appears that these profiles propagate by maintaining their shapes in spite of the disruption; this proves their stability. We have also investigated the impact of 30% noise level on the solutions stability. It reveals that, these solutions have extremely strong capacity of resisting disturbance with respect to higher initial noise level. We have also discussed the impact of the perturbed parameters such as inter-modal dispersion, self-steepening effect and Raman effect. Then, we draw the conclusion that the inter-modal dispersion influences the propagation velocity of the soliton. The self-steepening effect distorts the pulse such a way that it becomes asymmetric. The Raman effect leads to an unstable behavior for relatively small values.