A simple model based on the 1D nonlinear Schrodinger equation is studied, which contains both spatially and temporally dispersive terms. Parametric instabilities for plane waves are analyzed in detail, and solitary waves (both bright and dark) are found. The model presented here is able to describe the non-trivial unstable dynamics of intense, nonlinear light propagation near a material resonance in presence of negative spatial dispersion. We provide as a practical example the light propagation near the tail of an exciton-polariton resonance in a specially designed semiconductor superlattice. (C) 2008 Optical Society of America.