51 citations · 100 across the 8 of their papers we have counts for
9 papers
Existence of minimizers for the Dirac-Fock model of crystals
Isabelle Catto, Long Meng, Eric Paturel +1
Whereas many different models exist in the mathematical and physics literature for ground states of non-relativistic crystals, the relativistic case has been much less studied and…
On reducibility of Quantum Harmonic Oscillator on with quasiperiodic in time potential
Eric Paturel, Benoît Grébert
We prove that a linear d-dimensional Schr{ö}dinger equation on with harmonic potential and small t-quasiperiodic potential $i\partial\_t u -- Δu + |x|^2 u +…
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…
Modified scattering for the cubic Schr{ö}dinger equation on product spaces: the nonresonant case
Benoît Grébert, Eric Paturel, Laurent Thomann
We consider the cubic nonlinear Schr{ö}dinger equation on the spatial domain , and we perturb it with a convolution potential. Using recent technique…
Beating effects in cubic Schrödinger systems and growth of Sobolev norms
Benoît Grébert, Éric Paturel, Laurent Thomann
We consider a system of coupled cubic Schrödinger equations. We prove that there exists a beating effect, i.e. an energy exchange between different modes. This construction may be…
Birkhoff normal form and splitting methods for semi linear Hamiltonian PDEs. Part I: Finite dimensional discretization
Erwan Faou, Benoit Grebert, Eric Paturel
We consider {\em discretized} Hamiltonian PDEs associated with a Hamiltonian function that can be split into a linear unbounded operator and a regular nonlinear part. We consider s…