A semilinear Schroedinger equation with random potential

2019/03/08 by Marius Beceanu, Avy Soffer, Beceanu, Marius +1
Mathematics · Physics and Astronomy · #35J10 #35Q40 #35Q41 #60J65 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35J10 #msc:35Q40 #msc:35Q41 #msc:60J65

paper · pdf · doi:10.48550/arxiv.1903.03451

57 pages

arxiv created 2019/03/08 · arxiv updated 2019/03/11

Abstract

We study a non-linear Schroedinger equation with a Hartree-type nonlinearity and a localized random time-dependent external potential. Sharp dispersive estimates for the linear Schroedinger equation with a random time-dependent potential enable us to also treat the case of small semi-linear perturbations. In both the linear and the nonlinear instances, we prove that, on average, energy remains bounded and solutions scatter.

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