Standing waves of the Anderson-Gross-Pitaevskii equation
Analysis of PDEs
2025-12-30 v1 Mathematical Physics
math.MP
Probability
Abstract
In this paper, we study standing waves for the Anderson-Gross-Pitaevskii equation in dimension 1 and 2. The Anderson-Gross-Pitaevskii equation is a nonlinear Schr\"odinger equation with a confining potential and a multiplicative spatial white noise. Standing waves are characterized by a profile which is invariant by the dynamic and solves a nonlinear elliptic equation with spatial white noise potential. We construct such solutions via variational methods and obtain some results on their regularity, localization and stability.
Keywords
Cite
@article{arxiv.2512.22960,
title = {Standing waves of the Anderson-Gross-Pitaevskii equation},
author = {Samaël Mackowiak},
journal= {arXiv preprint arXiv:2512.22960},
year = {2025}
}