Solitons created by chirped initial profiles in coherent pulse propagation

"Solitons created by chirped initial profiles in coherent pulse propagation", L.V.Hmurcik and D.J.Kaup, Journal of the Optical Society of America, vol 69, p 597 (1979).If an incident pulse is chirped, the critical parameters for self-induced transparency to occur in coherent pulse propagation can no longer be obtained from the well-known McCall-Hahn area theorem. We have been able to obtain these parameters by solving the Zakharov-Shabat eigenvalue equation for the bound-state eigenvalues. We find that critical (threshold) areas will be increased for a chirped incident pulse in almost all cases, except for a box profile or for a pulse that is approximately box-like in shape. In these latter cases, the chirped critical areas will instead decrease for the second and all higher branches. The first branch’s critical area is always increased due to chirping