Stabilizing the Pereira-Stenflo solitons in nonlinear optical fibers

We study in detail stability of exact chirped solitary-pulse solutions in a model of a filtered nonlinear optical fiber, in which stabilization of the pulses is achieved by means of an extra lossy core, parallel-coupled to th e main one. We demonstrate that, in the model's three-dimensional parameter space, there is a vast region where the pulses are fully stable, for both signs of the group-velocity dispersion. These results open way to a stable transmission of optical solitons in the normal-dispersion region and, thus, to an essential expansion of the bandwidth offered by the nonlinear optica l fibers for telecommunications. In the cases when the pulses are unstable, we study the development of the instability, which may end up by either a blowup or decay to zero.