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arXiv · 1903.03451

A semilinear Schroedinger equation with random potential

Marius Beceanu·Avy Soffer
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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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Marius Beceanu, Avy Soffer. 2019-03-08. A semilinear Schroedinger equation with random potential. https://arxiv.org/abs/1903.03451

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