Approximation diffusion for the Nonlinear Schrödinger equation with a random potential

Article type: Research Article

Authors: Barrué, Grégoire^a | Debussche, Arnaud^{b; *} | Tusseau, Maxime^a

Affiliations: [a] Univ. Rennes, CNRS, IRMAR – UMR 6625, F-35000 Rennes, France | [b] Univ. Rennes & IUF, CNRS, IRMAR – UMR 6625, F-35000 Rennes, France

Correspondence: [*] Corresponding author. E-mail: arnaud.debussche@ens-rennes.fr.

Abstract: We prove that the stochastic Nonlinear Schrödinger (NLS) equation is the limit of NLS equation with random potential with vanishing correlation length. We generalize the perturbed test function method to the context of dispersive equations. Apart from the difficulty of working in infinite dimension, we treat the case of random perturbations which are not assumed uniformly bounded.

Keywords: Nonlinear Schrödinger equation, diffusion-approximation

DOI: 10.3233/ASY-241894

Journal: Asymptotic Analysis, vol. 138, no. 3, pp. 175-224, 2024