Zeitschrift für angewandte Mathematik und Physik ZAMP

, Volume 57, Issue 6, pp 905–939

Justification of the nonlinear Schrödinger equation in spatially periodic media

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

DOI: 10.1007/s00033-006-0057-6

Cite this article as:
Busch, K., Schneider, G., Tkeshelashvili, L. et al. Z. angew. Math. Phys. (2006) 57: 905. doi:10.1007/s00033-006-0057-6

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).

34C2035L0535Q60

Keywords.

Nonlinear wave equationperiodic media approximation by NLS

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
  4. 4.Institut für Theoretische FestkörperphysikUniversität KarlsruheKarlsruheGermany
  5. 5.Institut für NanotechnologieForschungszentrum Karlsruhe in der Helmholtz-GemeinschaftKarlsruheGermany