Optical soliton solutions in optical metamaterials with full nonlinearity

This paper derives optical soliton solutions for the nonlinear Schrödinger equation in optical metamaterials. A thorough examination of various nonlinearities is conducted, spanning those governed by the Kerr law, power law, parabolic law, dual power law, quadratic–cubic law, non-local law, and polynomial law. The optical soliton solutions are derived utilizing the addendum to Kudryashov’s method. Through the selection of specific parameter values, the analysis demonstrates the presence of straddled solutions, bright solitons, and singular solitons. Furthermore, the paper outlines the necessary conditions for the existence of soliton pulses. Additionally, the stability of the nonlinear Schrödinger equation with Kerr law nonlinearity is analyzed. Our results are compared with the related findings in the literature, underscoring the novelty and importance of our work.