Canonical coordinates with tame estimates for the defocusing NLS equation on the circle
Analysis of PDEs
2016-07-18 v1
Abstract
In a case study for integrable PDEs, we construct real analytic, canonical coordinates for the defocusing NLS equation on the circle, specifically taylored towards 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 dNLS Hamiltonian is in normal form up to order three.
Keywords
Cite
@article{arxiv.1607.04454,
title = {Canonical coordinates with tame estimates for the defocusing NLS equation on the circle},
author = {Thomas Kappeler and Riccardo Montalto},
journal= {arXiv preprint arXiv:1607.04454},
year = {2016}
}