12 citations · 19 across the 5 of their papers we have counts for
5 papers
Standing and Traveling Waves in a Nonlinearly Dispersive Lattice Model
Ross Parker, Pierre Germain, Jesús Cuevas-Maraver +2
In the work of Colliander et al. (2010), a minimal lattice model was constructed describing the transfer of energy to high frequencies in the defocusing nonlinear Schrödinger equat…
On the derivation of the homogeneous kinetic wave equation for a nonlinear random matrix model
Guillaume Dubach, Pierre Germain, Benjamin Harrop-Griffiths
We consider a nonlinear system of ODEs, where the underlying linear dynamics are determined by a Hermitian random matrix ensemble. We prove that the leading order dynamics in the w…
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…
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…