KAM for the Quantum Harmonic Oscillator


Por: Grébert B., Thomann L.

Publicada: 1 ene 2011
Resumen:
In this paper we prove an abstract KAM theorem for infinite dimensional Hamiltonians systems. This result extends previous works of S. B. Kuksin and J. Pöschel and uses recent techniques of H. Eliasson and S. B. Kuksin. As an application we show that some 1D nonlinear Schrödinger equations with harmonic potential admits many quasi-periodic solutions. In a second application we prove the reducibility of the 1D Schrödinger equations with the harmonic potential and a quasi periodic in time potential. © 2011 Springer-Verlag.

Filiaciones:
Grébert B.:
 Laboratoire de Mathématiques J. Leray, Université de Nantes, UMR CNRS 6629, 2, rue de la Houssiniére, 44322 Nantes Cedex 03, France

Thomann L.:
 Laboratoire de Mathématiques J. Leray, Université de Nantes, UMR CNRS 6629, 2, rue de la Houssiniére, 44322 Nantes Cedex 03, France
ISSN: 00103616
Editorial
SPRINGER, 233 SPRING ST, NEW YORK, NY 10013 USA, Estados Unidos America
Tipo de documento: Article
Volumen: 307 Número: 2
Páginas: 383-427
WOS Id: 000296650700004