Abstract
Optical wave propagation in an assembly of two-level atoms is considered. An asymptotic model of nonlinear Schr\"odinger (NLS) type is derived in a rigorous way by means of the perturbative expansion method. The results of the obtained model are then compared with both a numerical solution of the initial set of equations of the two-level model and an exact analytical cnoidal wave solution. It is seen that the evolution of the population difference is a key factor for the accurate determination of the nonlinear index, and that the NLS approximation allows one to determine it theoretically. The knowledge of the population difference allows one to correct the cnoidal wave solution, which then matches the numerical solution up to the limits of our numerical accuracy.
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