Hermite-Gaussian expansion for pulse propagation in strongly dispersion managed fibers

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Abstract
We represent a pulse in the strongly dispersion managed fiber as a linear superposition of Hermite-Gaussian harmonics, with the zeroth harmonic being a chirped Gaussian with periodically varying width. We obtain the same conditions for the stationary pulse propagation as were obtained earlier by the variational method. Moreover, we find a simple approximate formula for the pulse shape, which accounts for the numerically observed transition of that shape from a hyperbolic secant to the Gaussian. Finally, using the same approach, we systematically derive the equations for the evolution of a pulse under a general perturbation. This systematic derivation justifies the validity of similar equations obtained earlier from the conservation laws.