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

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

2012-02-16

arxiv.org/abs/1202.3671v2

Mathematics

Analysis of PDEs

Scientific paper

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 $O(1/\e)$. The leading terms of the WKB solutions solve cubic Schr\"odinger equations. We show that the nonlinear normal form method of Joly, M\'etivier and Rauch applies to this context. This implies that the Schr\"odinger approximation stays close to the exact solution of Maxwell-Landau-Lifshitz over its existence time. In the context of Maxwell-Landau-Lifshitz, this extends the analysis of Colin and Lannes from times $O(|\ln \e|)$ up to $O(1/\e)$.

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