  Nonlinear light propagation in a single-mode micron-size waveguide made of
semiconducting excitonic material has been theoretically studied in terms of
exciton-polaritons by using an analysis based on macroscopic fields. When a
light pulse is spectrally centered in the vicinity of the ground-state Wannier
exciton resonance, it interacts with the medium nonlinearly. This optical cubic
nonlinearity is caused by the repulsive exciton-exciton interactions in the
semiconductor, and at resonance it is orders of magnitude larger than the Kerr
nonlinearity (e.g., in silica). We demonstrate that a very strong and
unconventional modulational instability takes place, which has not been
previously reported. After reducing the problem to a single nonlinear
Schr\"odinger-like equation, we also explore the formation of solitary waves
both inside and outside the polaritonic gap and find evidence of spectral
broadening. A realistic physical model of the excitonic waveguide structure is
proposed.
