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.

中文翻译：

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两能级介质中的 Cnoidal 波：非线性磁化率的替代方法

我们考虑在两级系统中传播的 cnoidal 波，对此存在精确的解析解。描述克尔效应和三次谐波生成的三阶非线性的两个有效分量可以从中导出。关于非线性磁化率的通常形式，已经发现了一些差异。数值计算表明，精确的cnoidal波解最准确地描述了准单色波的非线性传播。特别是，没有观察到由非线性磁化率形式主义预测的三次非线性的三次谐波共振。