  The nonlinear optical properties of semiconductors near an excitonic
resonance are theoretically investigated by using the macroscopic J-model [Th.
Oestreich and A. Knorr, Phys. Rev. B 48, 17811 (1993); ibid. 50, 5717 (1994)]
based on the microscopic semiconductor Bloch equations. These nonlinear
properties cause modulational instability of long light pulses with large gain,
and give rise to a self-induced transmission of short light pulses in a
semiconductor. By an example of the latter well studied effect the validity of
the used macroscopic model is demonstrated and a good agreement is found with
both existing theoretical and experimental results.
