A semilinear Schroedinger equation with random potential
Analysis of PDEs
2019-03-11 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1903.03451,
title = {A semilinear Schroedinger equation with random potential},
author = {Marius Beceanu and Avy Soffer},
journal= {arXiv preprint arXiv:1903.03451},
year = {2019}
}
Comments
57 pages