Pure-Cubic Optical Soliton Solutions of the Nonlinear Schrödinger Equation Including Parabolic Law Nonlinearity in the Absence of the Group Velocity Dispersion

Abstract

This article investigates the third-order dimensionless nonlinear Schrödinger equation with a parabolic law media term, while deliberately excluding the group velocity dispersion term, which typically governs the propagation of ultrashort pulses. The Generalized Kudryashov approach, a powerful and novel technique, is applied for the first time to obtain pure-cubic optical soliton solutions for this model. Using this method, bright, kink, and dark soliton solutions are derived. To illustrate the dynamics and physical properties of these solutions, 2D, contour, and 3D visualizations are presented. In particular, 2D plots with carefully selected parameter values are provided to investigate how the presence of the parabolic law media term and the absence of the group velocity dispersion term influence soliton behavior. The results clearly demonstrate the physical relevance of the model and emphasize the effectiveness of the Generalized Kudryashov approach as a reliable technique for obtaining analytical solutions to the equation under consideration.