Stabilization of solitonlike pulses with a slow saturable absorber

We show that a soliton of the nonlinear Schrödinger equation perturbed by filter losses and/or the finite gain bandwidth of amplifiers can be kept stable by saturable absorbers with a relaxation time much longer than the width of the soliton. This provides for ultrashort pulse generation with a slow saturable absorber only and may have possible applications in the stabilization of soliton storage rings.