Quasiadiabatic following of femtosecond optical pulses in a weakly excited semiconductor

Using semiconductor Maxwell-Bloch equations, we analyze the response of an ensemble of $1s$ excitons driven by a femtosecond optical pulse beyond the traditional approach of slowly varying amplitudes and phases. For optical pulses of a given duration, we show that the off-resonance optical field can evolve into a stable soliton. Besides hyperbolic-secant solitons, we find a single soliton with nonzero asymptotics that is stable against low-amplitude perturbations and whose form is not affected by collisions.