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KAM tori for perturbations of the defocusing NLS equation
We prove that small, semi-linear Hamiltonian perturbations of the defocusing nonlinear Schrödinger (dNLS) equation on the circle have an abundance of invariant tori of any size and (finite) dimension which support quasi-periodic solutions. When compared with previous results the novelty consists in...
| Auteurs principaux : | , , |
|---|---|
| Format : | Livre |
| Langue : | anglais |
| Titre complet : | KAM tori for perturbations of the defocusing NLS equation / Massimiliano Berti, Thomas Kappeler, Riccardo Montalto |
| Publié : |
Paris :
Société mathématique de France
, 2018 |
| Description matérielle : | 1 vol. (VIII-148 p.) |
| Collection : | Astérisque ; 403 |
| Sujets : | |
| Documents associés : | Autre format:
KAM tori for perturbations of the defocusing NLS equation Fait partie de l'ensemble: Astérisque |
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| 200 | 1 | |a KAM tori for perturbations of the defocusing NLS equation |f Massimiliano Berti, Thomas Kappeler, Riccardo Montalto | |
| 210 | |a Paris |c Société mathématique de France |d 2018 | ||
| 215 | |a 1 vol. (VIII-148 p.) |d 25 cm | ||
| 300 | |a Erratum : le titre correct est : "Large KAM tori for perturbations of the defocusing NLS equation", information de la SMF, décembre 2018 | ||
| 302 | |a Résumés en anglais et français | ||
| 305 | |a N° de : "Astérisque", ISSN 0303-1179, (2018) n° 403 | ||
| 320 | |a Bibliogr. p. [145]-148 | ||
| 330 | |a We prove that small, semi-linear Hamiltonian perturbations of the defocusing nonlinear Schrödinger (dNLS) equation on the circle have an abundance of invariant tori of any size and (finite) dimension which support quasi-periodic solutions. When compared with previous results the novelty consists in considering perturbations which do not satisfy any symmetry condition (they may depend on x in an arbitrary way) and need not be analytic. The main difficulty is posed by pairs of almost resonant dNLS frequencies. The proof is based on the integrability of the dNLS equation, in particular the fact that the nonlinear part of the Birkhoff coordinates is one smoothing. We implement a Newton-Nash-Moser iteration scheme to construct the invariant tori. The key point is the reduction of linearized operators, coming up in the iteration scheme, to 2 x 2 block diagonal ones with constant coefficients together with sharp asymptotic estimates of their eigenvalues. [4e de couverture] | ||
| 452 | | | |0 232350191 |t KAM tori for perturbations of the defocusing NLS equation |f Massimiliano Berti, Thomas Kappeler, Riccardo Montalto |c Paris |n Société Mathématique de France |d 2018 | |
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