A variational method is used to study propagation of chirped op- tical pulses in media wit periodic amplification. A nonlinear resonance and chaos in oscillations of the pulse duration are considered. A sto- chastic instability of evolution of the pulse duration and also pulse decay under the influence of periodic amplification are predicted. A calculation is reported of the stochastic pulse-decay length and a comparison is made with the results of a numerical simulation. The applications of the results to long-haul optical communication lines with amplifiers and to optical fibres with a periodically modulated core dia- meter are considered.
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