A model of a long optical communication line consisting of alternating segm
ents with anomalous and normal dispersion, whose lengths are picked randoml
y from a certain interval, is considered. As the first stage of the analysi
s, we calculate small changes in parameters of a quasi-Gaussian pulse passi
ng a double-segment cell by means of the variational approximation (VA) and
we approximate the evolution of the pulse passing many cells by smoothed o
rdinary differential equations with random coefficients, which are solved n
umerically. Next we perform systematic direct simulations of the model. Sim
ulations reveal slow long-scale dynamics of the pulse, frequently in the fo
rm of long-period oscillations of its width. It is thus found that the soli
ton is most stable in the case of 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 soli
ton with low energy being much more robust than its high energy counterpart
. (C) 2001 Optical Society of America.