Velocity of the maximum of the envelope of a frequency-modulated Gaussian pulse in an amplifying nonlinear medium

The variation in the velocity of propagation of a narrowband frequency-modulated pulse in a nonlinear medium with dispersion of gain or absorption is studied. It is shown that the self-phase modulation caused by a cubic nonlinearity of the Kerr type can “accelerate” optical pulses of a Gaussian shape up to superluminal velocities even in the case where an initial frequency modulation (chirp) is absent.