Genovese, G., Lucà, R. and Valeri, D. (2016) Gibbs measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation. Selecta Mathematica - New Series, 22(3), pp. 1663-1702. (doi: 10.1007/s00029-016-0225-2)
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Abstract
We study the one-dimensional periodic derivative nonlinear Schrödinger equation. This is known to be a completely integrable system, in the sense that there is an infinite sequence of formal integrals of motion ∫hk , k∈Z+. In each ∫h2k the term with the highest regularity involves the Sobolev norm H˙k(T) of the solution of the DNLS equation. We show that a functional measure on L2(T) , absolutely continuous w.r.t. the Gaussian measure with covariance (I+(−Δ)k)−1, is associated to each integral of motion ∫h2k , k≥1 .
| 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: | Selecta Mathematica - New Series |
| Publisher: | Springer |
| ISSN: | 1022-1824 |
| ISSN (Online): | 1420-9020 |
| Published Online: | 19 March 2016 |
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