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Justification of the nonlinear Schrödinger equation in spatially periodic media |
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| Authors: | Kurt Busch Guido Schneider Lasha Tkeshelashvili Hannes Uecker |
| Affiliation: | 1. Department of Physics and College of Optics & Photonics, CREOL & FPCE, University of Central Florida, Orlando, FL, 32816, USA 2. Mathematisches Institut I, Universit?t Karlsruhe, D-76128, Karlsruhe, Germany 3. Mathematisches Institut I, Universit?t Karlsruhe, D-76128, Karlsruhe, Germany |
| Abstract: | 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 Schr?dinger equation. Here we prove estimates for the error made by this formal approximation using Bloch wave analysis, normal form transformations, and Gronwall’s inequality. |
| Keywords: | 34C20 35L05 35Q60 |
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