  We study the problem of propagation of an input electromagnetic pulse through
a long two-level laser amplifier under trivial initial conditions. In this
paper, we consider an unstable model described by the Maxwell-Bloch equations
without spectral broadening. Previously, this model was studied by S.V. Manakov
in 1982 and together with V.Yu. Novokshenov in 1986. We consider this model in
a more natural formulation as an initial-boundary (mixed) problem using a
modern version of the inverse scattering transform method in the form of a
suitable Riemann-Hilbert (RH) problem. The RH problem arises as a result of
applying the Fokas-Its method of simultaneous analysis of the corresponding
spectral problems for the Ablowitz-Kaup-Newell-Segur (AKNS) equations. This
approach makes it possible to obtain rigorous asymptotic results at large
times, which differ significantly from the previous ones. Differences take
place both near the light cone and in the tail region, where a new type of
solitons is found against an oscillating background. These solitons are
physically relevant, their velocities are smaller than the speed of light. The
number of such solitons can be either finite or infinite (in the latter case,
the set of zeros has a condensation point at infinity). Such solitons can not
be reflectionless, they are generated by zeros of the reflection coefficient of
the input pulse (and not by poles of the transmission coefficient).
  Thus our approach shows the presence of a new phenomenon in soliton theory,
namely, the boundary condition (input pulse) of a mixed problem under trivial
initial conditions can generate solitons due to the zeros of the reflection
coefficient, while the poles of the transmission coefficient do not contribute
to the asymptotics of the solution.
