Sobolev norms explosion for the cubic NLS on irrational tori

F Giuliani, M Guardia - Nonlinear Analysis, 2022 - Elsevier
We consider the cubic nonlinear Schrödinger equation on 2-dimensional irrational tori. We
construct solutions which undergo growth of Sobolev norms. More concretely, for every s> 0 …

Chaotic-like transfers of energy in Hamiltonian PDEs

F Giuliani, M Guardia, P Martin, S Pasquali - … in Mathematical Physics, 2021 - Springer
We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations
on T^ 2 T 2 and we prove the existence of different types of solutions which exchange …