  The Maxwell-Bloch system of equations with inhomogeneous broadening is
studied, and the local and global well-posedness of the corresponding
initial-boundary value problem is established by taking advantage of the
integrability of the system and making use of the corresponding inverse
scattering transform. A key ingredient in the analysis is the $L^2$-Sobolev
bijectivity of the direct and inverse scattering transform established by Xin
Zhou for the focusing Zakharov-Shabat problem.
