A note on stability of Eliasson-Kuksin's KAM tori for the nonlinear Schr\'{o}dinger equation
- Resource Type
- Working Paper
- Authors
- He, Xiaolong; Shi, Jia; Yuan, Xiaoping
- Source
- Subject
- Mathematics - Analysis of PDEs
Mathematics - Dynamical Systems
- Language
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.