Abstract
The problem of ultra-short-optical-pulse propagation through a two-level attenuating or amplifying atomic medium is considered where the optical pulse is a wave of permanent profile. It is shown that there are just four classes of such waves for each case of attenuator or amplifier and the eigenfunction-expansion technique is used to discuss their stability in laboratory time. For each case of attenuator or amplifier it is found that only one class of dynamic steady-state solutions is stable and that these stable solutions correspond to the propagation of an isolated 2π-pulse or a 2πn-pulse, wheren is infinite, through the attenuating or amplifying atomic medium. It is also shown how the stable dynamic steady-state isolated 2π-pulse for the attenuator or the amplifier may be generated from a constant background with the aid of Baecklund transformations.
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