Half-cycle soliton and periodic waves of arbitrarily high amplitude in a two-level system

We show that the electromagnetic wave propagation problem based on a two-level atomic model admits exact traveling wave solutions, of both soliton and cnoidal wave types. These solutions extend the already known solutions of the same type of both the mKdV and sG equations, which have been derived from the same initial model, respectively, in a long-wave and in a short-wave approximation. The continuation is such that no modification of the wave profile is required, but that the wave velocity only has to be corrected