  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.
