  We analyze the dynamics of dissipative solitons in silicon on insulator
waveguides embedded in a gain medium. The optical propagation is modeled
through a cubic Ginzburg-Landau equation for the field envelope coupled with an
ordinary differential equation accounting for the generation of free carriers
owing to two-photon absorption. Our numerical simulations clearly indicate that
dissipative solitons accelerate due to the carrier-induced index change and
experience a considerable blue-shift, which is mainly hampered by the gain
dispersion of the active material. Numerical results are fully explained by
analytical predictions based on soliton perturbation theory.
