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Dispersion management and the direct scattering transform.

It is shown that the direct scattering transform may be used to derive a perturbative theory of quasiperiodic field propagation in nonlinear fiber lines managed through zero-average, piecewise-constant dispersion maps. In this scheme, the field is propagated exactly and it is the quasiperiodicity property which is approximated. The resulting quasiperiodicity conditions are shown to agree with the dispersion managed nonlinear Schrödinger equation up to order 4.