Justification of the nonlinear Schrödinger equation in spatially periodic media
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The dynamics of the envelopes of spatially and temporarily oscillating wave packets advancing in spatially periodic media can approximately be described by solutions of a Nonlinear Schrödinger equation. Here we prove estimates for the error made by this formal approximation using Bloch wave analysis, normal form transformations, and Gronwall’s inequality.
Mathematics Subject Classification (2000).34C20 35L05 35Q60
Keywords.Nonlinear wave equation periodic media approximation by NLS
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