Genovese, G., Lucà, R. and Valeri, D. (2019) Invariant measures for the periodic derivative nonlinear Schrödinger equation. Mathematische Annalen, 374(3-4), pp. 1075-1138. (doi: 10.1007/s00208-018-1754-0)
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Abstract
We construct invariant measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation (DNLS) for small data in L2 and we show these measures to be absolutely continuous with respect to the Gaussian measure. The key ingredient of the proof is the analysis of the gauge group of transformations associated to DNLS. As an intermediate step for our main result, we prove quasi-invariance with respect to the gauge maps of the Gaussian measure on L2 with covariance (I+(−Δ)k)−1 for any k⩾2.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Valeri, Dr Daniele |
| Authors: | Genovese, G., Lucà, R., and Valeri, D. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Mathematische Annalen |
| Publisher: | Springer |
| ISSN: | 0025-5831 |
| ISSN (Online): | 1432-1807 |
| Published Online: | 21 September 2018 |
| Copyright Holders: | Copyright © 2018 Springer-Verlag GmbH Germany, part of Springer Nature |
| First Published: | First published in Mathematische Annalen 374(3-4):1075-1138 |
| Publisher Policy: | Reproduced in accordance with the copyright policy of the publisher |
| Related URLs: |
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