Chaotic resonant dynamics and exchanges of energy in Hamiltonian PDEs

Autor: Stefano Pasquali, Pau Martín, Marcel Guardia, Filippo Giuliani

Publikováno v: Rendiconti Lincei - Matematica e Applicazioni. 32:149-166

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 energy among Fourier modes in a \emph{chaotic-like} way. We say that a tra

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::695e5dd52ff86cd942142c9f13f58306
https://doi.org/10.4171/rlm/931

Sobolev norms explosion for the cubic NLS on irrational tori

Autor: Filippo Giuliani, Marcel Guardia

Publikováno v: Nonlinear Analysis. 220:112865

We consider the cubic nonlinear Schr��dinger equation on $2$-dimensional irrational tori. We construct solutions which undergo growth of Sobolev norms. More concretely, for every $s>0$, $s\neq 1$ and almost every choice of spatial periods we cons

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9d4be00e89e5eb3abb3f90738f03484d
https://doi.org/10.1016/j.na.2022.112865

Chaotic-like transfers of energy in hamiltonian PDEs

Autor: Filippo Giuliani, Stefano Pasquali, Marcel Guardia, Pau Martín

Publikováno v: Communications in Mathematical Physics
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations on T2 and we prove the existence of different types of solutions which exchange energy between Fourier modes in certain time scales. This exchange can be conside

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1351839967fd9eb1a2f971bb8778ead6
https://hdl.handle.net/2117/363923

Time Quasi-Periodic Traveling Gravity Water Waves in Infinite Depth

Autor: 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 first existence result of quasi-periodic water waves solutions bifurcatin

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6babdcc5194e02563ffffc70eda7310e

On the integrability of Degasperis-Procesi equation: control of the Sobolev norms and Birkhoff resonances

Autor: Filippo Giuliani, Roberto Feola, Stefano Pasquali

Publikováno v: RECERCAT (Dipòsit de la Recerca de Catalunya)
Recercat. Dipósit de la Recerca de Catalunya
instname
Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)

We consider the dispersive Degasperis–Procesi equation u t − u x x t − c u x x x + 4 c u x − u u x x x − 3 u x u x x + 4 u u x = 0 with c ∈ R ∖ { 0 } . In [15] the authors proved that this equation possesses infinitely many conserved qu

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::673deccb58534df19ebb8b4a41ccc9eb
http://arxiv.org/abs/1802.00035