Conditions for stationary pulse propagation in the strong dispersion management regime

Using the variational method, we obtain analytical conditions for stationary propagation of a Gaussian pulse in a fibre with strong dispersion management. We consider both the lossless fibre and the one with losses and periodic amplification. The analytical predictions have been checked against direct numerical simulations, and a good agreement between the two has been demonstrated. In particular, we find that in a certain region of parameters, the average dispersion necessary to support the stationary propagation is negative (normal). We also show that under a certain assumption, the variance of the Gordon-Haus timing jitter for the pulse in a strongly dispersion-managed system approximately equals that for the conventional soliton, reduced by an energy enhancement factor. Using our analytical conditions, we obtain an estimate for this factor. In particular, we show that in the presence of losses and periodic amplification, this jitter suppression factor can be made to be as large as that for the lossless case, by properly choosing the segment lengths in the dispersion map.