We present the recent result in [29] concerning strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite-gap solutions of the defocusing cubic nonlinear Schrodinger 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 construct solutions of the 2D cubic NLS that start arbitrarily close to such invariant tori in the H-s topology (0 < s < 1) and whose H-s norm can grow by any given factor.

A note on growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation / Guardia, Marcel; Hani, Zaher; Haus, Emanuele; Maspero, Alberto; Procesi, Michela. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - 30:4(2019), pp. 865-880. [10.4171/RLM/873]

A note on growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation

Maspero, Alberto;
2019

Abstract

We present the recent result in [29] concerning strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite-gap solutions of the defocusing cubic nonlinear Schrodinger 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 construct solutions of the 2D cubic NLS that start arbitrarily close to such invariant tori in the H-s topology (0 < s < 1) and whose H-s norm can grow by any given factor.
30
4
865
880
https://www.ems-ph.org/journals/show_abstract.php?issn=1120-6330&amp;vol=30&amp;iss=4&amp;rank=8
Guardia, Marcel; Hani, Zaher; Haus, Emanuele; Maspero, Alberto; Procesi, Michela
File in questo prodotto:
File Dimensione Formato  
RLM-2019-030-004-08.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Non specificato
Dimensione 149.6 kB
Formato Adobe PDF
149.6 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
NotaGHHMP.pdf

accesso aperto

Tipologia: Documento in Post-print
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 469.62 kB
Formato Adobe PDF
469.62 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/106101
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 1
social impact