A KAM algorithm for the resonant non-linear Schrödinger equation

By C. Procesi, Michela Procesi. 2012

138 citations recorded by the source corpus.

Abstract We prove, through a KAM algorithm, the existence of large families of stable and unstable quasi-periodic solutions for the NLS in any number of independent frequencies. The main tools are the existence of a non-degenerate integrable normal form proved in [26] , [27] and a generalization of the quasi-Toplitz functions defined in [31] .

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d012aad539d089ed9e8e027d30831258210eed0a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Massimiliano Berti
2. Michela Procesi
3. Livia Corsi
4. Riccardo Montalto

In Statistical and Nonlinear Physics

1. Massimiliano Berti
2. Michela Procesi
3. Livia Corsi
4. P. Bolle
5. Riccardo Montalto
6. Pierre Baldi
7. E. Haus
8. C. Procesi

Citations in the corpus

• An Abstract Nash–Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds (2013, background): “Then Geng-Xu-You [16] proved KAM results for the cubic NLS in dimension 2 and Procesi-Procesi [24] in any dimension n and polynomial nonlinearity.”