  We theoretically investigate the free-carrier induced spatio-temporal
dynamics of continuous waves in silicon waveguides embedded in an amplifying
medium. Optical propagation is governed by a cubic Ginzburg-Landau equation
coupled with an ordinary differential equation accounting for the free-carrier
dynamics. We find that, owing to free-carrier dispersion, countinuous waves are
modulationally unstable in both anomalous and normal dispersion regimes and
chaotically generate unstable accelerating pulses.
