Implicit Quiescent Optical Soliton Perturbation with Nonlinear Chromatic Dispersion and Kudryashov’s Self-Phase Modulation Structures for the Complex Ginzburg–Landau Equation Using Lie Symmetry: Linear Temporal Evolution

This paper investigates quiescent solitons in optical fibers and crystals, modeled by the complicated Ginzburg–Landau equation incorporating nonlinear chromatic dispersion and six self-phase modulation structures introduced by Kudryashov. The model is formulated with linear temporal evolution and analyzed using Lie symmetry methods. The study also identified parameter constraints under which solutions exist.