10 citations · 10 across the 2 of their papers we have counts for
5 papers
Growth of Sobolev norms for abstract linear Schrödinger Equations
Dario Bambusi, Benoit Grébert, Alberto Maspero +1
We prove an abstract theorem giving a bound () on the growth of the Sobolev norms in linear Schrödinger equations of the form $i \dot ψ= H_0 ψ+ V(…
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 +…
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…
Normal form theory for the NLS equation
Benoît Grébert, Thomas Kappeler, Jürgen Pöschel
We consider the nonlinear Schrodinger equation with a cubic nonlinearity on the circle, which is known to represent an integrable Hamiltonian system. We construct a global coordina…