Stable autosolitons in dispersive media with saturable gain and absorption

We introduce the simplest one-dimensional model of a dispersive optical med ium with saturable dissipative nonlinearity and filtering (dispersive loss) which gives rise to stable solitary pulses (autosolitons). In the particul ar case when the dispersive loss is absent, the same model may also be inte rpreted as describing a stationary field in a planar optical waveguide with uniformly distributed saturable gain and absorption. In a certain region o f the model's parameter space, two coexisting solitary-pulse solutions are found numerically, one of which may be stable. Solving the corresponding li nearized eigenvalue problem, we identify stability borders for the solitary pulses in their parametric plane. Beyond one of the borders, the symmetric pulse is destroyed by asymmetric perturbations, and at the other border it undergoes a Hopf bifurcation, which may turn it into a breather. (C) 2000 Elsevier Science B.V. All rights reserved.