Inverse scattering transform for 3-level coupled Maxwell-Bloch equations with inhomogeneous broadening

In this paper we study the propagation of optical pulses in an optical medium with coherent three-level atomic transitions. The interaction between the pulses and the medium is described by the coupled Maxwell-Bloch equations, which we investigate by applying the method of inverse scattering transform. The details of the inverse scattering method and the non-trivial evolution of the associated scattering data are discussed. The one- and two-soliton solutions, polarization shifts due to two-soliton interactions, and the explicit form of the transmission matrix associated with pure soliton solutions are also derived.