Abstract
We consider a cnoidal wave propagating in a two-level system, for which an exact analytic solution exists. Two effective components of the third-order nonlinearity , describing Kerr effect and third harmonics generation, can be derived from it. Some discrepancy has been found with respect to the usual formalism of nonlinear susceptibilities. Numerical computation shows that the exact cnoidal wave solution the most accurately describes the nonlinear propagation of a quasi-monochromatic wave. Especially, the third harmonic resonance of the third-order nonlinearity, predicted by the formalism of nonlinear susceptibilities, is not observed.
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