Abstract
The dynamics of pulse propagation through nonlinear optical metamaterials, maintaining parabolic law nonlinearity, is investigated. The model includes spatio-temporal dispersion, detuning effect, inter-modal dispersion, self-steepening effect, Raman scattering, nonlinear dispersion and third-order dispersion. Bright, dark and singular soliton solutions are derived by the implementation of coupled phase-amplitude formulation. The conditions on the material parameters for the existence of these solitons are also enumerated.