61 citations · 61 across the 3 of their papers we have counts for
5 papers
Stationary martingale solution for the 2D stochastic Gross-Pitaevskii equation
Anne de Bouard, Arnaud Debussche, Reika Fukuizumi
In this short report we give a proof of the existence of a stationary solution to the Gross-Pitaevskii equation in driven by a space-time white noise.
Two dimensional Gross-Pitaevskii equation with space-time white noise
Anne de Bouard, Arnaud Debussche, Reika Fukuizumi
In this paper we consider the two-dimensional stochastic Gross-Pitaevskii equation, which is a model to describe Bose-Einstein condensation at positive temperature. The equation is…
Long time behavior of Gross-Pitaevskii equation at positive temperature
Anne de Bouard, Arnaud Debussche, Reika Fukuizumi
The stochastic Gross-Pitaevskii equation is used as a model to describe Bose-Einstein condensation at positive temperature. The equation is a complex Ginzburg Landau equation with…
Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise
Anne De Bouard, Arnaud Debussche
We consider a randomly perturbed Korteweg-de Vries equation. The perturbation is a random potential depending both on space and time, with a white noise behavior in time, and a reg…
Blow-up for the stochastic nonlinear Schrodinger equation with multiplicative noise
Anne de Bouard, Arnaud Debussche
We study the influence of a multiplicative Gaussian noise, white in time and correlated in space, on the blow-up phenomenon in the supercritical nonlinear Schrodinger equation. We…