Advances in Mathematical Physics
Volume 2011 (2011), Article ID 854719, 4 pages
http://dx.doi.org/10.1155/2011/854719
Research Article

Justification of the NLS Approximation for the KdV Equation Using the Miura Transformation

Guido Schneider

IADM, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany

Received 4 March 2011; Accepted 16 March 2011

Academic Editor: Pavel Exner

Copyright © 2011 Guido Schneider. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

It is the purpose of this paper to give a simple proof of the fact that solutions of the KdV equation can be approximated via solutions of the NLS equation. The proof is based on an elimination of the quadratic terms of the KdV equation via the Miura transformation.