"Non UBC"@en .
"DSpace"@en .
"Emanuele Haus"@en .
"2019-12-09T10:13:23Z"@en .
"2019-06-11T16:31"@en .
"We consider the defocusing cubic nonlinear Schr\u00C3 \u00C2\u00B6dinger 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."@en .
"https://circle.library.ubc.ca/rest/handle/2429/72597?expand=metadata"@en .
"42.0 minutes"@en .
"video/mp4"@en .
""@en .
"Author affiliation: Universit\u00E0 di Napoli Federico II"@en .
"Oaxaca (Mexico : State)"@en .
"10.14288/1.0386792"@en .
"eng"@en .
"Unreviewed"@en .
"Vancouver : University of British Columbia Library"@en .
"Banff International Research Station for Mathematical Innovation and Discovery"@en .
"Attribution-NonCommercial-NoDerivatives 4.0 International"@en .
"http://creativecommons.org/licenses/by-nc-nd/4.0/"@en .
"Researcher"@en .
"BIRS Workshop Lecture Videos (Oaxaca (Mexico : State))"@en .
"Mathematics"@en .
"Dynamical Systems And Ergodic Theory, Partial Differential Equations"@en .
"Strong Sobolev instability of quasi-periodic solutions of the 2D cubic Schr\u00C3 \u00C2\u00B6dinger equation"@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/72597"@en .