Self-induced transparency and the soliton lattice

The propagation of a step-function light pulse in a nondamping resonant medium is studied. Numerical analysis and conservation laws show that the asymptotic solution cannot be described by a single solition-lattice-type solution. As the pulses propagate in space they become narrower and with larger amplitude, but the time separation between pulses remains constant. This result is explained by an asymptotic area theorem which restricts the time average of the electric field to be equal to that of the imput field.