The period map for pulse propagation in nonlinear optical DM fibres

We have derived a simple recursion formula for the amplitude and chirp of the optical pulse propagating over a Dispersion Managed fibre 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 nonlinear Schrödinger 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 non-soliton initial pulses. Matching them through the interfaces of the legs we get recursion formulas for the pulse amplitude and chirp. Our analytical results are well justified by numerical simulations.