Exploring of soliton solutions in optical metamaterials with parabolic law of nonlinearity

In this article, we examine the nonlinear Schrödinger equation governing the dynamics of electromagnetic pulse in metamaterials revealing a parabolic law of nonlinearity. The Sub-sardar equation method is used to examine and comprehend the solutions to the nonlinear Schrödinger equation better. This method allows one to derive dark, bright, singular-bright, and periodic solitons, among other types of soliton solutions. The complex dynamics of electromagnetic pulses in metamaterials are largely dependent on soliton dynamics, which are stable, localized wave packets that preserve their amplitude and shape during propagation. Metamaterials are engineered materials with unique electromagnetic properties not found in nature, and studying the dynamics of electromagnetic pulses within them is essential for advancing applications in fields such as optics and telecommunications. Additionally, the study conducts stability and sensitivity analyses for the obtained results, going beyond theoretical derivations. To facilitate the visual understanding of the solutions the 3D, 2D and contour graphs of achieved solutions are also presented.