@article{f20e4dd72eed44a5a6b1e65025ee7223,
title = "On the problem of dynamical localization in the nonlinear Schr{\"o}dinger equation with a random potential",
abstract = "We prove a dynamical localization in the nonlinear Schr{\"o}dinger equation with a random potential for times of the order of O(β -2), where β is the strength of the nonlinearity.",
keywords = "Anderson localization, Dynamical localization, NLSE, Nonlinear Schr{\"o}dinger, Random potential",
author = "Shmuel Fishman and Yevgeny Krivolapov and Avy Soffer",
note = "Funding Information: Acknowledgements This work was partly supported by the Israel Science Foundation (ISF), by the US-Israel Binational Science Foundation (BSF), by the USA National Science Foundation (NSF), by the Minerva Center of Nonlinear Physics of Complex Systems, by the Shlomo Kaplansky academic chair, by the Fund for promotion of research at the Technion and by the E. and J. Bishop research fund. The work was done partially while SF was visiting the Institute of Mathematical Sciences, National University of Singapore in 2006 and the Center of Nonlinear Physics of Complex Systems in Dresden in 2007 and while YK visited the department of Mathematics at Rutgers University and while AS was visiting the Lewiner Institute of Theoretical Physics at the Technion in 2007. The visits were supported in part by these Institutes. It is our great pleasure to thank M. Aizenman for extremely illuminating, critical and detailed discussions. Highly instructive discussions with S. Aubry, I. Guarneri, S. Flach, A. Klein and W.M. Wang are acknowledged.",
year = "2008",
month = jun,
day = "1",
doi = "10.1007/s10955-007-9472-0",
language = "English",
volume = "131",
pages = "843--865",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",
number = "5",
}