Anderson localisation for the nonlinear Schroedinger Equation (NLSE): results and puzzles
Seminar Room 1, Newton Institute
AbstractThe NLSE is relevant for the explorations of Bose-Einstein Condensates and for Nonlinear Classical Optics. A natural question is whether Anderson Localization survives the effect of nonlinearities in one dimension. Relevant experimental, numerical, heuristic and rigorous results will be presented. A perturbation expansion in the nonlinear term was developed 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. Conjectures on the long time behavior will be presented. The work reported in the talk was done in collaboration with Avy Soffer and Yevgeny Krivolapov.
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