Non UBC
DSpace
Emanuele Haus
2019-12-09T10:13:23Z
2019-06-11T16:31
We consider the defocusing cubic nonlinear SchrÃ Â¶dinger equation (NLS) on the two-dimensional torus. This equation admits a special family of elliptic invariant quasiperiodic tori called finite-gap solutions. These solutions 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 timescales, they exhibit a strong form of transverse instability in Sobolev spaces H^s(T^2) (0 < s < 1). More precisely, we construct solutions of the 2D cubic NLS that start arbitrarily close to such invariant tori in the H^s topology and whose H^s norm can grow by any given factor. In my talk, I will also say some words about the ongoing work concerning Sobolev instability of more general 2D quasi-periodic solutions. The subject of this talk is partly motivated by the problem of infinite energy cascade for 2D NLS, and it is a joint work with M. Guardia, Z. Hani, A. Maspero and M. Procesi.
https://circle.library.ubc.ca/rest/handle/2429/72597?expand=metadata
42.0 minutes
video/mp4
Author affiliation: Università di Napoli Federico II
Oaxaca (Mexico : State)
10.14288/1.0386792
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Researcher
BIRS Workshop Lecture Videos (Oaxaca (Mexico : State))
Mathematics
Dynamical Systems And Ergodic Theory, Partial Differential Equations
Strong Sobolev instability of quasi-periodic solutions of the 2D cubic SchrÃ Â¶dinger equation
Moving Image
http://hdl.handle.net/2429/72597