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We consider the evolution of optical solitons inside a nonlinear dispersive fiber with random birefringence, causing polarization-mode dispersion. We convert the pair of coupled nonlinear Schrö dinger equations satisfied by the orthogonally polarized components into a Fokker-Planck equation using the collective-variable approach. We solve this equation and derive expressions for the probability density functions associated with the differential group delay and the pulse width in the limit ofdoi:10.1103/physrevlett.90.013902 pmid:12570611 fatcat:vqfzgm2m6bgwhatiqyugyhbzo4