10 citations · 18 across the 11 of their papers we have counts for
18 papers
Global Well-Posedness and Uniform Long-Time Control for a Class of Periodic NLS-Dysthe Equations
Andrea Belloni, Filippo Giuliani
We study a class of periodic NLS-Dysthe (NLS-Dy) equations, also referred to as higher-order nonlinear Schrödinger equations (HNLS), of the form $i\partial_t u+a\partial_x^2u+b|u|^…
Long time strong Sobolev instability for quasilinear NLS
Yuri Cacchiò, Filippo Giuliani, Felice Iandoli +1
We prove long-time strong Sobolev instability for a class of quasilinear Schrödinger equations on arising, via the Madelung transform, in the description of Euler-Kor…
Sobolev instability in the cubic NLS equation with convolution potentials on irrational tori
Filippo Giuliani
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…
Local well posedness for a system of quasilinear pdes modelling suspension bridges
Roberto Feola, Filippo Giuliani, Felice Iandoli +1
In this paper we provide a local well posedness result for a quasilinear beam-wave system of equations on a one-dimensional spatial domain under periodic and Dirichlet boundary con…
Effective chaos for the Kirchhoff equation on tori
Pietro Baldi, Filippo Giuliani, Marcel Guardia +1
We consider the Kirchhoff equation on tori of any dimension and we construct solutions whose Sobolev norms oscillates in a chaotic way on certain long time scales. The chaoticity i…
Long time NLS approximation for the quasilinear Klein-Gordon equation on large domains under periodic boundary conditions
Roberto Feola, Filippo Giuliani
We provide the rigorous justification of the NLS approximation, in Sobolev regularity, for a class of quasilinear Hamiltonian Klein Gordon equations with quadratic nonlinearities o…
Arnold diffusion in Hamiltonian systems on infinite lattices
Filippo Giuliani, Marcel Guardia
We consider a system of infinitely many penduli on an -dimensional lattice with a weak coupling. For any prescribed path in the lattice, for suitable couplings, we construct orb…
Sobolev norms explosion for the cubic NLS on irrational tori
Filippo Giuliani, Marcel Guardia
We consider the cubic nonlinear Schrödinger equation on -dimensional irrational tori. We construct solutions which undergo growth of Sobolev norms. More concretely, for every $s…
Time Quasi-Periodic Traveling Gravity Water Waves in Infinite Depth
Roberto Feola, Filippo Giuliani
We present the recent result [8] concerning the existence of quasi-periodic in time traveling waves for the 2d pure gravity water waves system in infinite depth. We provide the fir…
Chaotic Resonant Dynamics and Exchanges of Energy in Hamiltonian PDEs
Filippo Giuliani, Marcel Guardia, Pau Martin +1
The aim of this note is to present the recent results in [16] where we provide the existence of solutions of some nonlinear resonant PDEs on the 2-dimensional torus exchanging ener…
Transfers of energy through fast diffusion channels in some resonant PDEs on the circle
Filippo Giuliani
In this paper we consider two classes of resonant Hamiltonian PDEs on the circle with non-convex (respect to actions) first order resonant Hamiltonian. We show that, for appropriat…
Chaotic-like transfers of energy in Hamiltonian PDEs
Filippo Giuliani, Marcel Guardia, Pau Martin +1
We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations on and we prove the existence of different types of solutions which exchange energy b…
Quasi-periodic traveling waves on an infinitely deep fluid under gravity
Roberto Feola, Filippo Giuliani
We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth and we establish the existence and the linear stability of small amplitude, q…
Reducible KAM tori for Degasperis-Procesi equation
Roberto Feola, Filippo Giuliani, Michela Procesi
We develop KAM theory close to an elliptic fixed point for quasi-linear Hamiltonian perturbations of the dispersive Degasperis-Procesi equation on the circle. The overall strategy…
Reducibility for a class of weakly dispersive linear operators arising from the Degasperis Procesi equation
Roberto Feola, Filippo Giuliani, Michela Procesi
We prove reducibility of a class of quasi-periodically forced linear equations of the form \[ \partial_tu-\partial_x\circ (1+a(ωt, x))u+\mathcal{Q}(ωt)u=0,\quad x\in\mathbb{T}:=\ma…
On the integrability of Degasperis-Procesi equation: control of the Sobolev norms and Birkhoff resonances
Roberto Feola, Filippo Giuliani, Stefano Pasquali
We consider the dispersive Degasperis-Procesi equation with . In \cite{Deg} t…
Reducibility of first order linear operators on tori via Moser's theorem
Roberto Feola, Filippo Giuliani, Riccardo Montalto +1
In this paper we prove reducibility of classes of linear first order operators on tori by applying a generalization of Moser's theorem on straightening of vector fields on a torus.…
Quasi-periodic solutions for quasi-linear generalized KdV equations
Filippo Giuliani
We prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear autonomous Hamiltonian generalized KdV equations. We conside…