Period Map for Nonlinear Pulses in Optical Dispersion-Managed Fibers

We derive a simple recursion formula for the amplitude and chirp of the optical pulse propagating over a dispersion-managed fiber with zero mean dispersion. We neglect dissipation and assume the dispersion to be constant along the adjacent legs of the waveguide, thus providing the applicability of the integrable NLS models within each leg. Choosing the legs to be long enough to ensure the formation of a self-similar profile, we apply the well-known asymptotic formulas for the nonsoliton initial pulses. Matching them through the interfaces of the legs, we obtain the recursion formulas for the pulse amplitude and the chirp. Our analytic results are well justified by numerical simulations.