Modulation instability and extraction of fractional optical solitons in the presence of generalized Kudryashov’s law and dual form of non-local nonlinearity

• Published in: Physica scripta 2024-07, Vol.99 (7)
• Main Authors: Chahlaoui, Younes, Umair, Muhammad, Butt, Asma Rashid, Alshahrani, Alanoud A M
• Format: Article
• Language: English
• Subjects: conformable fractional derivative; expansion methods; generalized exp; Kudryashov’s law of nonlinear refractive index; perturbed terms; quadrupled-power law
• ISSN: 0031-8949; 1402-4896
• DOI: 10.1088/1402-4896/ad51b3

This research delves into the study of optical solitons governed by Kudryashov’s law of nonlinear refractive index, incorporating a conformable fractional derivative, perturbed terms, and a quadrupled-power law in optical fibers. Employing a novel approach known as the generalized exp(-S(ζ)) expansion method, we identify novel op tical soliton solutions characterized by exponential, rational, and hyperbolic functions. These solutions manifest as kink, anti-kink, singular, singular periodic, unified bright dark solitons, and solitary waves. Through graphical representations, we analyze the behavior of these solutions across various fractional-order derivative parameters, offer ing insights into their physical interpretations. Furthermore, we conduct modulation instability (MI) analysis based on standard linear stability analysis to obtain the MI gain spectrum, highlighting the effectiveness of our methodology in addressing nonlinear challenges across engineering and natural sciences domains. Our study underscores the potential for practical applications and further research in this field.