Optical soliton solutions, stability, and modulation instability for fractional multi-components of Gross–Pitaevskii model

This study investigates the soliton solutions of the fractional multi-component Gross–Pitaevskii model, a pivotal framework in quantum engineering and nonlinear optics, particularly for its applications in optical fibers. By introducing the ρ-derivative to manage fractional components, we employ two potent analytical techniques: the modified Kudryashov method and the F(ξ)G(ξ) expansion method. These methods successfully yield a diverse spectrum of soliton solutions, including rational, combined dark–bright, and mixed trigonometric forms. To elucidate the physical characteristics of these solutions, we present both two and three-dimensional graphical representations. Furthermore, we analyze the model’s modulation instability to assess its stability under small perturbations. The resulting instability growth rates are also visualized graphically, providing a comprehensive understanding of the model’s dynamical behavior.