Features of evolution of a 0π pulse in a medium with an inhomogeneously broadened resonance quantum transition

The results of numerical simulations are outlined for the evolution of a 0π pulse in a medium with an inhomogeneously broadened quantum transition neglecting irreversible relaxation. A rule is formulated for the prediction of the 0π-pulse structure at long distances, which relies on the notion of the 0π-pulse area as the area under the curve of the modulus of its envelope. Analytical relations between the duration, the peak value, and the propagation velocity are given for the 0π pulse of the breather type.