Abstract
This work studies the optical solitons in optical nonlinear metamaterials. The parabolic law nonlinearity, spatio-temporal dispersion, inter-modal dispersion, self-steepening as well as nonlinear dispersion are taken into account. Two integration approaches that are Ricatti equation expansion method and ansatz scheme are adopted to obtain optical solitons. Finally, analytical dark soliton, bright soliton, singular soliton as well as singular periodic solutions are reported. The corresponding constraint conditions in order for these exact solutions to exist are derived.