â€” In this paper we consider supercritical nonlinear SchrÃ¶dinger equations in an analytic Riemannian manifold (M, g), where the metric g is analytic. Using an analytic WKB method, we are able toâ€¦ (More)

â€” In this article, we first present the construction of Gibbs measures associated to nonlinear SchrÃ¶dinger equations with harmonic potential. Then we show that the corresponding Cauchy problem isâ€¦ (More)

We consider the continuous resonant (CR) system of the 2D cubic nonlinear SchrÃ¶dinger (NLS) equation. This system arises in numerous instances as an effective equation for the long-time dynamics ofâ€¦ (More)

â€” Using variational methods, we construct approximate solutions for the Gross-Pitaevski equation which concentrate on circles in R. These solutions will help to show that the L flow is unstable forâ€¦ (More)

â€” In this paper we construct a Gibbs measure for the derivative SchrÃ¶dinger equation on the circle. The construction uses some renormalisations of Gaussian series and Wiener chaos estimates, ideasâ€¦ (More)

â€” In this paper we consider the SchrÃ¶dinger equation with powerlike nonlinearity and confining potential or without potential. This equation is known to be well-posed with data in a Sobolev space Hâ€¦ (More)

â€” We extend a randomisation method, introduced by Shiffman-Zelditch and developed by Burq-Lebeau on compact manifolds for the Laplace operator, to the case of R with the harmonic oscillator. Weâ€¦ (More)

â€” Thanks to an approach inspired from Burq-Lebeau [6], we prove stochastic versions of Strichartz estimates for SchrÃ¶dinger with harmonic potential. As a consequence, we show that the nonlinearâ€¦ (More)

Let (M, g) be a Riemannian surface (i.e. a Riemannian manifold of dimension 2), orientable or not. We assume that M is either compact or a compact perturbation of the euclidian space, so that theâ€¦ (More)