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.accessioned
2024-09-19T14:25:23Z
dc.date.available
2023-06-21T13:41:52Z
dc.date.available
2024-09-19T14:25:23Z
dc.date.issued
2022-03-03
dc.identifier.uri
http://hdl.handle.net/2072/535459
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.
eng
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.
cat
dc.publisher
European Mathematical Society Publishing House
cat
dc.relation.ispartof
Journal of the European Mathematical Society
cat
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
cat
dc.title
Strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite gap tori for the 2D cubic NLS equation
cat
dc.type
info:eu-repo/semantics/article
cat
dc.type
info:eu-repo/semantics/publishedVersion
cat
dc.identifier.doi
10.4171/JEMS/1200
cat
dc.rights.accessLevel
info:eu-repo/semantics/openAccess
