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We describe the only two significant effects of the residual birefringence of high-quality fibers on solitons in long-distance transmission: a possible gradual accumulation of differential transit time between orthogonally polarized solitons and a jitter in pulse arrival times, initiated by noise modulation of the polarization states of the pulses and mediated by the birefringence.
Mollenauer et al. (Tue,) studied this question.