29 citations · 115 across the 11 of their papers we have counts for
11 papers
Inhomogeneous turbulence for the Wick nonlinear Schrödinger equation
Zaher Hani, Jalal Shatah, Hui Zhu
We introduce a simplified model for wave turbulence theory -- the Wick NLS, of which the main feature is the absence of all self-interactions in the correlation expansions of its s…
Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrödinger equation
Tristan Buckmaster, Pierre Germain, Zaher Hani +1
Consider the cubic nonlinear Schrödinger equation set on a d-dimensional torus, with data whose Fourier coefficients have phases which are uniformly distributed and independent. We…
Scattering for the 3D Gross-Pitaevskii equation
Zihua Guo, Zaher Hani, Kenji Nakanishi
We study the Cauchy problem for the 3D Gross-Pitaevskii equation. The global well-posedness in the natural energy space was proved by Gérard \cite{Gerard}. In this paper we prove s…
Analysis of the (CR) equation in higher dimensions
T. Buckmaster, P. Germain, Z. Hani +1
This paper is devoted to the analysis of the continuous resonant (CR) equation, in dimensions greater than 2. This equation arises as the large box (or high frequency) limit of the…
Effective dynamics of the nonlinear Schrödinger equation on large domains
Tristan Buckmaster, Pierre Germain, Zaher Hani +1
We consider the nonlinear Schrödinger (NLS) equation posed on the box with periodic boundary conditions. The aim is to describe the long-time dynamics by deriving effecti…
On the continuous resonant equation for NLS: II. Statistical study
Pierre Germain, Zaher Hani, Laurent Thomann
We consider the continuous resonant (CR) system of the 2D cubic nonlinear Schr{ö}dinger (NLS) equation. This system arises in numerous instances as an effective equation for the lo…