Justification of the nonlinear Schrödinger equation in spatially periodic media

  • Kurt Busch
  • Guido Schneider
  • Lasha Tkeshelashvili
  • Hannes Uecker
Article

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 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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Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  • Kurt Busch
    • 1
  • Guido Schneider
    • 2
  • Lasha Tkeshelashvili
    • 1
  • Hannes Uecker
    • 3
  1. 1.Department of Physics and College of Optics & Photonics, CREOL & FPCEUniversity of Central FloridaOrlandoUSA
  2. 2.Mathematisches Institut IUniversität KarlsruheKarlsruheGermany
  3. 3.Mathematisches Institut IUniversität KarlsruheKarlsruheGermany

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