60 citations · 68 across the 8 of their papers we have counts for
9 papers
Almost global existence for Hamiltonian PDEs on compact manifolds
Dario Bambusi, Joackim Bernier, Benoît Grébert +1
We prove an abstract result of almost global existence of small solutions to semi-linear Hamiltonian partial differential equations satisfying very weak non resonance conditions an…
Infinite dimensional invariant tori for nonlinear Schrödinger equations
Joackim Bernier, Benoit Grébert, Tristan Robert
We prove that nonlinear Schrödinger equations on the circle, without external parameters, admits plenty of almost periodic solutions. Indeed, we prove that arbitrarily close to mos…
Longtime dynamics for the Landau Hamiltonian with a time dependent magnetic field
Dario Bambusi, Benoit Grébert, Alberto Maspero +2
We consider a modulated magnetic field, , perpendicular to a fixed plane, where is constant, and a periodic function on the…
Exponential stability of solutions to the Schr{ö}dinger-Poisson equation
Joackim Bernier, Nicolas Camps, Benoît Grébert +1
We prove an exponential stability result for the small solutions of the Schr{ö}dinger-Poisson equation on the circle without exterior parameters in Gevrey class. More precisely we…
Dynamics of quintic nonlinear Schr{ö}dinger equations in
Joackim Bernier, Benoît Grébert, Tristan Robert
In this paper, we succeed in integrating Strichartz estimates (encoding the dispersive effects of the equations) in Birkhoff normal form techniques. As a consequence, we deduce a r…
Almost global existence for some nonlinear Schr{ö}dinger equations on in low regularity
Joackim Bernier, Benoît Grébert
We are interested in the long time behavior of solutions of the nonlinear Schr{ö}dinger equation on the -dimensional torus in low regularity, i.e. for small initial data in the…
Discrete pseudo-differential operators and applications to numerical schemes
Erwan Faou, Benoît Grébert
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can de…
Existence and stability of solitons for fully discrete approximations of the nonlinear Schrödinger equation
Dario Bambusi, Erwan Faou, Benoit Grebert
In this paper we study the long time behavior of a discrete approximation in time and space of the cubic nonlinear Schrödinger equation on the real line. More precisely, we conside…
A Nekhoroshev type theorem for the nonlinear Schrödinger equation on the d-dimensional torus.
Erwan Faou, Benoit Grebert
We prove a Nekhoroshev type theorem for the nonlinear Schrödinger equation $$ iu_t=-Δu+V\star u+\partial_{\bar u}g(u,\bar u)\, \quad x\in \T^d, $$ where is a typical smooth pot…