We consider the cubic defocusing nonlinear Schrödinger equation on the two-dimensional
torus. Fix s> 1. Recently Colliander, Keel, Staffilani, Tao and Takaoka proved the existence …

In this paper we prove an abstract KAM theorem for infinite dimensional Hamiltonians
systems. This result extends previous works of SB Kuksin and J. Pöschel and uses recent …

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 …

We study dynamical properties of the cubic lowest Landau level equation, which is used in
the modeling of fast rotating Bose–Einstein condensates. We obtain bounds on the decay of …

We prove that a linear d-dimensional Schrödinger equation on Rd with harmonic potential|
x| 2 and small t-quasiperiodic potential i∂ tu−∆ u+| x| 2u+ εV (tω, x) u= 0, x∈ Rd reduces to …

We study the quintic nonlinear Schrödinger equation on a two-dimensional torus and exhibit
orbits whose Sobolev norms grow with time. The main point is to reduce to a sufficiently …

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 …

We study the long time behavior of small solutions of semi-linear dispersive Hamiltonian
partial differential equations on confined domains. Provided that the system enjoys a new …

We introduce specific solutions to the linear harmonic oscillator, named bubbles. They form
resonant families of invariant tori of the linear dynamics, with arbitrarily large Sobolev norms …

We provide an accurate description of the long time dynamics of the solutions of the
generalized Korteweg–De Vries and Benjamin–Ono equations on the one dimension torus …