Kappeler, Thomas; Montalto, Riccardo (2018). Canonical coordinates with tame estimates for the defocusing NLS equation on the circle. International Mathematics Research Notices, 2018(5):1473-1531.
In a case study for integrable PDEs, we construct real analytic, canonical coordinates for the defocusing NLS equation on the circle, specifically tailored to the needs in perturbation theory. They are defined in neighbourhoods of families of finite-dimensional invariant tori and are shown to satisfy together with their derivatives tame estimates. When expressed in these coordinates, the defocusing NLS Hamiltonian is in normal form up to order three.
In a case study for integrable PDEs, we construct real analytic, canonical coordinates for the defocusing NLS equation on the circle, specifically tailored to the needs in perturbation theory. They are defined in neighbourhoods of families of finite-dimensional invariant tori and are shown to satisfy together with their derivatives tame estimates. When expressed in these coordinates, the defocusing NLS Hamiltonian is in normal form up to order three.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > General Mathematics |
| Language: | English |
| Date: | 26 December 2018 |
| Deposited On: | 23 Jan 2019 12:59 |
| Last Modified: | 30 Nov 2023 08:14 |
| Publisher: | Oxford University Press |
| ISSN: | 1073-7928 |
| OA Status: | Green |
| Publisher DOI: | https://doi.org/10.1093/imrn/rnw233 |
Kappeler, Thomas