Delving into quasi-periodic type optical solitons in fully nonlinear complex structured perturbed Gerdjikov–Ivanov equation

• Published in: Scientific reports Vol. 15; no. 1; pp. 8818 - 19
• Main Authors: Yan, Zhimin, Li, Jinbo, Barak, Shoaib, Haque, Salma, Mlaiki, Nabil
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 14.03.2025; Nature Publishing Group; Nature Portfolio
• Subjects: 639/705; 639/705/1041; Algebra; Fiber optics; Fibers; Fractals; Humanities and Social Sciences; Investigations; Mathematics; multidisciplinary; Nonlinear partial differential equations; Optical soliton; Ordinary differential equations; Partial differential equations; Periodic perturbation; Perturbed Gerdjikov–Ivanov equation; Riccati modified extended simple equation method; Science; Science (multidisciplinary); Perturbed Gerdjikov–Ivanov equation; Riccati modified extended simple equation method; Nonlinear partial differential equations; Periodic perturbation; Optical soliton
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/s41598-025-91978-x

In this study, we aim to explore the soliton phenomena in fully nonlinear complex perturbed Gerdjikov–Ivanov equation (PGIE). This model concerns with optical pulse transmission pursuant to perturbation impacts encompassing significant uses in optical fibers, especially, photonic crystal fibers. We employ the Riccati modified extended simple equation method, which has never been employed for this model previously, to acquire novel and distinct optical soliton solutions. To visually evaluate the dynamics of derived optical soliton solutions, several 3D, 2D, and contour graphics are incorporated. These visuals reveal a range of quasi-periodic type optical soliton phenomena, that include internal envelope, hump, cnoidal, periodic, and fractal solitons. In addition to including additional soliton dynamics into the model, the results show how these dynamics interact to affect the system’s overall behavior.