Hybrid computational analysis of fractional optical soliton structures in a dispersive Schrödinger model with applications in nonlinear optics

The present study aims to integrate and explore optical solitary wave solutions within the framework of the high-order fractional dispersive extended nonlinear Schrödinger model (FDENLSM), a refined mathematical formulation with wide-ranging applications in nonlinear physics, optical communications, and field theory. By utilizing three contemporary computational approaches, namely, the modified Sardar sub-equation method, the new Kudryashov approach, and the improved F-expansion method, we obtain and systematically analyze a rich spectrum of optical soliton structures, including dark, singular, bright, periodic, exponential, rational, and composite forms. Furthermore, distinct wave patterns such as W-shaped, bell-shaped, peakon, and mixed trigonometric–hyperbolic solitons are also investigated. The study extends to the examination of modulation instability and gain spectra of the FDENLSM, providing deeper insight into the system’s nonlinear characteristics. To vividly signify the obtained results, contour and density maps are presented in both two- and three-dimensional perspectives. The outcomes of this research contribute significantly to the understanding of complex nonlinear propagation phenomena, offering valuable analytical tools for researchers working in plasma dynamics, fiber optics, and related nonlinear systems.