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KAM tori in 1D random discrete nonlinear Schrodinger model?
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics . Linköping University, The Institute of Technology.ORCID iD: 0000-0001-6708-1560
University of Crete.
CEA Saclay.
2010 (English)In: EPL, ISSN 0295-5075, Vol. 91, no 5Article in journal (Refereed) Published
Abstract [en]

We suggest that KAM theory could be extended for certain infinite-dimensional systems with purely discrete linear spectrum. We provide empirical arguments for the existence of square summable infinite-dimensional invariant tori in the random discrete nonlinear Schrodinger equation, appearing with a finite probability for a given initial condition with sufficiently small norm. Numerical support for the existence of a fat Cantor set of initial conditions generating almost periodic oscillations is obtained by analyzing i) sets of recurrent trajectories over successively larger time scales, and ii) finite-time Lyapunov exponents. The norm region where such KAM-like tori may exist shrinks to zero when the disorder strength goes to zero and the localization length diverges.

Place, publisher, year, edition, pages
EDP Sciences. , 2010. Vol. 91, no 5
National Category
Medical and Health Sciences
Identifiers
URN: urn:nbn:se:liu:diva-60251DOI: 10.1209/0295-5075/91/50001ISI: 000282123300001OAI: oai:DiVA.org:liu-60251DiVA: diva2:355829
Note
Original Publication: Magnus Johansson, G Kopidakis and S Aubry, KAM tori in 1D random discrete nonlinear Schrodinger model?, 2010, EPL, (91), 5. http://dx.doi.org/10.1209/0295-5075/91/50001 Copyright: EDP Sciences. http://publications.edpsciences.org/ Available from: 2010-10-08 Created: 2010-10-08 Last updated: 2014-01-13

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
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  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
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  • nn-NB
  • sv-SE
  • Other locale
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Output format
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