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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Busch, K., Schneider, G., Tkeshelashvili, L. et al. Justification of the nonlinear Schrödinger equation in spatially periodic media. Z. angew. Math. Phys. 57, 905–939 (2006). https://doi.org/10.1007/s00033-006-0057-6
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00033-006-0057-6