We consider the propagation of chirped optical solitons in a fiber with periodic dispersion and describe this by a variational approach assuming a single pulse ansatz. We obtain a good agreement between the variational equations and the full numerical solution for the low-frequency region below the fundamental resonance. In that case we study the nonlinear resonances and chaotic oscillations of the pulse width and with this analysis we can predict the stochastic decay of pulses under a periodic modulation of the dispersion. For the main resonance and resonances above it, this simple variational approach fails because of a strong emission of linear waves. Then the numerical solution decays slowly while the simple model predicts a fast breakup. In the high-frequency limit the pulse is stable and we can describe it via averaged variational equations for its width and chirp, which we derive. We show that this dynamical model yields interesting physical estimates for soliton propagation in a fiber with dispersion management. [S1063-651X(98)12110-4]. [References: 30]
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