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arXiv · 2105.12333

A note on stability of Eliasson-Kuksin's KAM tori for the nonlinear Schr\"{o}dinger equation

Xiaolong He·Jia Shi·Xiaoping Yuan
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Abstract

Eliasson and Kuksin developed a KAM approach to study the persistence of the invariant tori for nonlinear Schr\"{o}dinger equation on $\mathbb{T}^{d}$. In this note, we improve Eliasson and Kuksin's KAM theorem by using Kolmogorov's iterative scheme and obtain a local normal form for the transformed Hamiltonian. As a consequence, we are able to derive the time $\delta^{-1}$ stability of the obtained KAM tori.

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Xiaolong He, Jia Shi, Xiaoping Yuan. 2021-05-26. A note on stability of Eliasson-Kuksin's KAM tori for the nonlinear Schr\"{o}dinger equation. https://arxiv.org/abs/2105.12333

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