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
Canonical Coordinates with Tame Estimates for the Defocusing NLS Equation on the Circle / T. Kappeler, R. Montalto. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2018:5(2018 Mar 06), pp. 1473-1531.
Canonical Coordinates with Tame Estimates for the Defocusing NLS Equation on the Circle
R. Montalto
2018
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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