Analytical Study of Perturbed Nonlinear SchröDinger Equations: Optical Soliton Dynamics Via Generalized Abel Equation and Collective Variables Approaches

In this study, we deal with the perturbed nonlinear Schr & ouml;dinger equation (PNLSE). This equation is an important model for describing optical soliton propagation in nonlinear optical fibers with the Kerr law nonlinearity. Two efficient techniques are employed: the generalized Abel equation method (GAEM) with variable coefficients and the collective variable (CV) approach. As a consequence of GAEM, we derive a periodic-type soliton solution and enhance its physical interpretation through graphical simulations. The CV method, carrying a fourth-order Runge-Kutta scheme and the Gaussian ansatz, is used to model the dynamics of soliton parameters such as amplitude, width, chirp, and frequency, revealing periodic fluctuations influenced by propagation distance. Both methods provide a comprehensive understanding of soliton behaviors in optical fibers, offering valuable outcomes for advancing optical communication systems.