In this paper we prove a result of almost global existence for some abstract nonlinear PDEs
on flat tori and apply it to some concrete equations, namely a nonlinear Schrödinger …

We analyze the energy transfer for solutions to the defocusing cubic nonlinear Schr\"
odinger (NLS) initial value problem on 2D irrational tori. Moreover we complement the …

We build a smooth real potential V (t, x) on (t 0,+∞)× R 2 decaying to zero as t→∞ and a
smooth solution to the associated perturbed cubic noninear harmonic oscillator whose …

In this paper we consider linear, time dependent Schrödinger equations of the form i∂ t ψ=
K 0 ψ+ V (t) ψ, where K 0 is a strictly positive selfadjoint operator with discrete spectrum and …

In this paper we prove the existence of solutions to the cubic NLS equation with convolution
potentials on two dimensional irrational tori undergoing an arbitrarily large growth of …

We consider the problem of transfer of energy to high frequencies in a quasilinear Schr\"
odinger equation with sublinear dispersion, on the one dimensional torus. We exhibit initial …

In this paper we consider the linear, time-dependent quantum Harmonic Schr<? TeX {\" o}?>
dinger equation,, where is classical pseudodifferential operator of order 0, self-adjoint, and …

We consider nonlinear Schr\" odinger equations on flat tori satisfying a simple and explicit
Diophantine non-degeneracy condition. Provided that the nonlinearity contains a cubic term …

We study analytically the dynamics of a $ d $-dimensional Klein-Gordon lattice with periodic
boundary conditions, for $ d\leq 3$. We consider initial data supported on one low-frequency …

In the last three decades there is an intense activity on the exploration of turbulent
phenomena of dispersive equations, as for instance the growth of Sobolev norms since the …