Sub- and superluminal kink-like waves in the kinetic limit of Maxwell–Bloch equations

Running-wave solutions to three systems of partial differential equations describing wave propagation in atomic media in the kinetic limit have been obtained. Those systems include approximations to (i) standard two-level Maxwell–Bloch equations; (ii) equations describing processes with saturated absorption in three-level systems and (iii) equations describing processes with reversed saturation in four-level systems. It has been shown that in all three cases kink-like solitary waves can emerge if the dynamical equation for the intensity includes a linear contribution to the Lambert–Beer law. Those solitary waves can propagate with either subor superluminal velocity of the edge of the kink, and in a direction which can be either the same as or opposite to that of the carrier wave. In addition, simple qualitative information about the behaviour of waves near the wavefronts has been obtained. PACS numbers: 42.25.Bs, 42.65.−k, 42.50.Gy