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Canonical coordinates with tame estimates for the defocusing NLS equation on the circle


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.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:26 December 2018
Deposited On:23 Jan 2019 12:59
Last Modified:24 Sep 2019 23:58
Publisher:Oxford University Press
ISSN:1073-7928
OA Status:Green
Publisher DOI:https://doi.org/10.1093/imrn/rnw233

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