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

2012/02/16 by Yong Lu, Yong, LU
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #Quantum Chromodynamics and Particle Interactions #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.1202.3671

openalex publication_date 2012/02/16 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We study semilinear Maxwell-Landau-Lifshitz systems in one space dimension.\nFor highly oscillatory and prepared initial data, we construct WKB approximate\nsolutions over long times O(1/ e). The leading terms of the WKB solutions\nsolve cubic Schr "odinger equations. We show that the nonlinear normal form\nmethod of Joly, M 'etivier and Rauch applies to this context. This implies that\nthe Schr "odinger approximation stays close to the exact solution of\nMaxwell-Landau-Lifshitz over its existence time. In the context of\nMaxwell-Landau-Lifshitz, this extends the analysis of Colin and Lannes from\ntimes O(|\ln e|) up to O(1/ e).\n

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