44 citations · 170 across the 35 of their papers we have counts for
9 papers · 1 filter
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…
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…
On small breathers of nonlinear Klein-Gordon equations via exponentially small homoclinic splitting
Otávio M. L. Gomide, Marcel Guardia, Tere M. Seara +1
Breathers are nontrivial time-periodic and spatially localized solutions of nonlinear dispersive partial differential equations (PDEs). Families of breathers have been found for ce…
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…
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…
Strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation
Marcel Guardia, Zaher Hani, Emanuele Haus +2
We consider the defocusing cubic nonlinear Schrödinger equation (NLS) on the two-dimensional torus. The equation admits a special family of elliptic invariant quasiperiodic tori ca…
Growth of Sobolev norms for the analytic NLS on
Marcel Guardia, Emanuele Haus, Michela Procesi
We consider the completely resonant defocusing non-linear Schrödinger equation on the two dimensional torus with any analytic gauge invariant nonlinearity. Fix . We show the e…
Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation with a convolution potential
Marcel Guardia
Fix . Colliander, Keel, Staffilani, Tao and Takaoka proved in \cite{CollianderKSTT10} the existence of solutions of the cubic defocusing nonlinear Schrödinger equation in the…
Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation
Marcel Guardia, Vadim Kaloshin
We consider the cubic defocusing nonlinear Schrödinger equation in the two dimensional torus. Fix . Colliander, Keel, Staffilani, Tao and Takaoka proved in \cite{CollianderKST…