Propagation effects in superfluorescence

The evolution of a superfluorescent pulse is studied in the region of large sample lengths. A solution to the Maxwell-Bloch semiclassical equations is found by using the inverse scattering method. It has the form of a one-soliton solution with varying parameters. Dependence on the pulse width and the retarded time is found without further approximations. These parameters are shown to be independent of the inhomogeneous broadening time. Their values are in good agreement with experiment. Asymmetry of the pulse is also investigated.