dc.contributor.author |
Guardia, M. |
dc.contributor.author |
Hani, Z. |
dc.contributor.author |
Haus, E. |
dc.contributor.author |
Maspero, A. |
dc.contributor.author |
Procesi, M. |
dc.date.accessioned |
2023-06-21T13:41:52Z |
dc.date.available |
2023-06-21T13:41:52Z |
dc.date.issued |
2022-03-03 |
dc.identifier.uri |
http://hdl.handle.net/2072/535459 |
dc.description.sponsorship |
National Science Foundation, NSF: DMS-1600561, DMS-1654692; Horizon 2020 Framework Programme, H2020: 757802; FP7 Ideas: European Research Council, IDEAS-ERC: 306414; European Research Council, ERC; Federación Española de Enfermedades Raras, FEDER: PGC2018-098676-B-100; Ministerio de Economía y Competitividad, MINECO; Institució Catalana de Recerca i Estudis Avançats, ICREA. Funding. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 757802) and under FP7-IDEAS (grant agreement No 306414). M.G. has also been partly supported by the Spanish MINECO-FEDER Grant PGC2018-098676-B-100 (AEI/FEDER/UE) and by the Catalan Institution for Research and Advanced Studies via an ICREA Academia Prize 2019. Z.H. was partly supported by a Sloan Fellowship, NSF grants DMS-1600561 and DMS-1654692, and a Simons Collaboration Grant. A.M. was partly supported by Progetto di Ricerca GNAMPA - INdAM 2018 “Moti stabili ed instabili in equazioni di tipo Schrödinger”. M.P. and E.H. were partially supported by PRIN 2015 “Variational methods in analysis, geometry and physics”. |
dc.format.extent |
55 p. |
dc.language.iso |
eng |
dc.publisher |
European Mathematical Society Publishing House |
dc.relation.ispartof |
Journal of the European Mathematical Society |
dc.rights |
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: https://creativecommons.org/licenses/by/4.0/ |
dc.source |
RECERCAT (Dipòsit de la Recerca de Catalunya) |
dc.subject.other |
growth of Sobolev norms; KAM; Nonlinear Schrödinger equation; quasiperiodic; stability |
dc.title |
Strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite gap tori for the 2D cubic NLS equation |
dc.type |
info:eu-repo/semantics/article |
dc.type |
info:eu-repo/semantics/publishedVersion |
dc.embargo.terms |
cap |
dc.identifier.doi |
10.4171/JEMS/1200 |
dc.rights.accessLevel |
info:eu-repo/semantics/openAccess |
dc.description.abstract |
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 called finite gap solutions. These are inherited from the integrable 1D model (cubic NLS on the circle) by considering solutions that depend only on one variable. We study the long-time stability of such invariant tori for the 2D NLS model and show that, under certain assumptions and over sufficiently long time scales, they exhibit a strong form of transverse instability in Sobolev spaces Hs.T2/ (0 < s < 1). More precisely, we construct solutions of the 2D cubic NLS that start arbitrarily close to such invariant tori in the Hs topology and whose Hs norm can grow by any given factor. This work is partly motivated by the problem of infinite energy cascade for 2D NLS, and seems to be the first instance where (unstable) long-time nonlinear dynamics near (linearly stable) quasiperiodic tori is studied and constructed. © 2023 European Mathematical Society Publishing House. All rights reserved. |