Coherent vector pi-pulse in optical amplifiers

We obtain an exact vector solitary solution for the amplification of an optical pulse with a time width short compared with both population and polarization decay time. This dissipative soliton results from the balance between the gain from inverted resonant two-level atoms and the linear loss of the host material. We suppose that the excited state of the active centers is degenerate on the projection of the angular moment. Numerical simulations demonstrate the stability of these vector dissipative solitons in the presence of both linear birefringence and group velocity dispersion of the host material.