Investigation of chirped solutions in optical metamaterials having parabolic law nonlinearity and space-time dispersion

Based on the nonlinear Schrödinger equation, we investigate the exact nonlinear chirps of the dynamic model for the propagation of optical solitons in nonlinear metamaterials. The trial equation method and the complete discrimination system for polynomial method are utilized to construct dark soliton, bright soliton, kink soliton, anti-kink soliton, Jacobi elliptic function solutions, as well as singular rational and singular biperiodic solutions. Notably, we have derived new solutions in the forms of the kink soliton, anti-kink soliton, and Jacobi elliptic function. Therefore, we provide a comprehensive categorization of all solutions, along with the parameter requirements for determining their existence. Furthermore, we also receive corresponding amplitude and chirp graphs for specific physical parameters, which aid in understanding the propagation characteristics of chirped solutions in optical metamaterials.