  A model of a long optical communication line consisting of alternating
segments with anomalous and normal dispersion, whose lengths are picked up
randomly from a certain interval, is considered. At the first stage of the
analysis, we calculate small changes of parameters of a quasi-Gaussian pulse
passing a two-segment cell by means of the variational approach (VA), and
approximate the evolution of the pulse passing many cells by smoothed ODEs with
random coefficients, which are then solved numerically. Next, we perform
systematic direct simulations of the model. Results are presented as
dependences of the pulse's mean width, and standard deviation of the width from
its mean value, on the propagation distance. The results produced by VA and
direct simulations are similar. Averaging over 200 different realizations of
the random-length set reveals slow long-scale dynamics of the pulse, frequently
in the form of long-period oscillations of its width. It is thus found that the
soliton is most stable in the case of the zero path-average dispersion (PAD),
less stable in the case of anomalous PAD, and least stable in the case of
normal PAD. The soliton's stability also strongly depends on its energy, the
soliton with small energy being much more robust than its large-energy
counterpart.
