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SUMMARY:Anderson localisation for the nonlinear Schroedinger Equation (NLS
 E): results and puzzles - Fishman\, S (Technion)
DTSTART:20080822T090000Z
DTEND:20080822T100000Z
UID:TALK13158@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The NLSE is relevant for the explorations of Bose-Einstein Con
 densates and for Nonlinear Classical Optics. A natural question is whether
  Anderson Localization survives the effect of nonlinearities in one dimens
 ion. Relevant experimental\, numerical\, heuristic and rigorous results wi
 ll be presented. A perturbation expansion in the nonlinear term was develo
 ped and used to obtain a rigorous bound on the spreading for short times. 
 In particular it is found that exponential localization holds at least for
  time scales inversely proportional to the square of the nonlinearity. Con
 jectures on the long time behavior will be presented.\n\nThe work reported
  in the talk was done in collaboration with Avy Soffer and Yevgeny Krivola
 pov.
LOCATION:Seminar Room 1\, Newton Institute
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