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Russian Mathematical Surveys, 2004, Volume 59, Issue 2, Pages 231–246
DOI: https://doi.org/10.1070/RM2004v059n02ABEH000716 (Mi rm716) 		 
This article is cited in 29 scientific papers (total in 29 papers)

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

J. Bourgain

Institute for Advanced Study, School of Mathematics
English version PDF (255 kB) Citations (29)
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DOI: https://doi.org/10.1070/RM2004v059n02ABEH000716
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.
Received: 23.01.2004
Russian version:
Uspekhi Matematicheskikh Nauk, 2004, Volume 59, Issue 2(356), Pages 37–52
DOI: https://doi.org/10.4213/rm716
Bibliographic databases:
Document Type: Article
UDC: 517.984+517.958
MSC: Primary 35Q55; Secondary 35J10, 35L05, 37K99, 82B44, 37N20, 47B39
Language: English
Original paper language: Russian
Citation: J. Bourgain, “Recent progress on quasi-periodic lattice Schrödinger operators and Hamiltonian PDEs”, Uspekhi Mat. Nauk, 59:2(356) (2004), 37–52; Russian Math. Surveys, 59:2 (2004), 231–246
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/rm/v59/i2/p37
    • This publication is cited in the following 29 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Успехи математических наук Russian Mathematical Surveys
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    Abstract page:981
    Russian version PDF:328
    English version PDF:35
    References:79
    First page:3
     
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