114 citations · 451 across the 22 of their papers we have counts for
25 papers
Long time behavior of the solutions of NLW on the d-dimensional torus
Joackim Bernier, Erwan Faou, Benoit Grebert
We consider the non linear wave equation (NLW) on the d-dimensional torus with a smooth nonlinearity of order at least two at the origin. We prove that, for almost any mass, small…
Rational normal forms and stability of small solutions to nonlinear Schrödinger equations
Joackim Bernier, Erwan Faou, Benoit Grebert
We consider general classes of nonlinear Schrödinger equations on the circle with nontrivial cubic part and without external parameters. We construct a new type of normal forms, na…
Reducibility of the Quantum Harmonic Oscillator in -dimensions with Polynomial Time Dependent Perturbation
Dario Bambusi, Benoit Grebert, Alberto Maspero +1
We prove a reducibility result for a quantum harmonic oscillator in arbitrary dimensions with arbitrary frequencies perturbed by a linear operator which is a polynomial of degree t…
A Kam Theorem for Space-Multidimensional Hamiltonian PDE
L Hakan Eliasson, Benoit Grebert, Sergei Kuksin
We present an abstract KAM theorem, adapted to space-multidimensional hamiltonian PDEs with smoothing non-linearities. The main novelties of this theorem are that: the in…
KAM for the nonlinear beam equation
L. Hakan Eliasson, Benoît Grébert, Sergei B. Kuksin
In this paper we prove a KAM theorem for small-amplitude solutions of the non linear beam equation on the d-dimensional torus $$u_{tt}+Δ^2 u+m u + \partial_u G(x,u)=0\ ,\quad t\in…
KAM for the Klein Gordon equation on
Benoît Grébert, Eric Paturel
Recently the KAM theory has been extended to multidimensional PDEs. Nevertheless all these recent results concern PDEs on the torus, essentially because in that case the correspond…