We study in detail stability of exact chirped solitary-pulse solutions in a model in which stabilization of the pulses is achieved by means of short segments of an extra lossy core, which is parallel coupled to the main one. We demonstrate that, in the model’s three-dimensional parameter space, there is a vast region in which the pulses are fully stable, for both signs of the group-velocity dispersion. These results open the way to a stable transmission of solitary optical pulses in the normal-dispersion region and thus to an essential expansion of the bandwidth offered by the nonlinear optical fibers for telecommunications in the return-to-zero regime. In the cases in which the pulses are unstable, we study the development of the instability, which may end by either blowing up or decaying to zero. In the case when the pulses are stable, we also simulate interactions between them, concluding that they always eventually merge into one pulse.
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