High-frequency limit of the Maxwell-Landau-Lifshitz system in the diffractive optics regime

We study semilinear Maxwell-Landau-Lifshitz systems in one space dimension. For highly oscillatory and prepared initial data, we construct WKB approximate solutions over long times O(1/ε). The leading terms of the WKB solutions solve cubic Schrödinger equations. We show that the nonlinear normal form method of Joly, Métivier and Rauch [5] applies to this context. This implies that the Schrödinger approximation stays close to the exact solution of MaxwellLandau-Lifshitz over diffractive times. In the context of Maxwell-Landau-Lifshitz, this extends the analysis of Colin and Lannes [3] from times O(| ln ε|) up to O(1/ε).