This article is cited in 29 papers

Recent progress on quasi-periodic lattice Schrödinger operators and Hamiltonian PDEs

J. Bourgain

Institute for Advanced Study, School of Mathematics

Abstract: This is a survey of recent investigations of quasi-periodic localization on lattices (of both methods based on perturbation theory and non-perturbative methods) and of applications of KAM theories in connection with infinite-dimensional Hamiltonian systems. The focus is on applications of these investigations to the Schrödinger equation and the wave equation with periodic boundary conditions, and to non-linear random Schrödinger equations with short-range potentials.

UDC: 517.984+517.958

MSC: Primary 35Q55; Secondary 35J10, 35L05, 37K99, 82B44, 37N20, 47B39

Received: 23.01.2004

DOI: 10.4213/rm716

 English version: Russian Mathematical Surveys, 2004, 59:2, 231–246

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