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

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ProjectHamInstab - Instabilities and homoclinic phenomena in Hamiltonian systems (EC-H2020-757802)
DINAMICA ASOCIADA A CONEXIONES ENTRE OBJETOS INVARIANTES CON APLICACIONES A NEUROCIENCIA Y ASTRODINAMICA (MINECO-MTM2015-65715-P)

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 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 construct solutions of the 2D cubic NLS that start arbitrarily close to such invariant tori in the Hs topology (0 < s < 1) and whose Hs norm can grow by any given factor.

CitationGuardia, M. [et al.]. A note on growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation. "Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni", 1 Gener 2019, vol. 30, núm. 4, p. 865-880.

URIhttp://hdl.handle.net/2117/181664

DOI10.4171/RLM/873

ISSN1120-6330

Publisher versionhttps://www.ems-ph.org/journals/show_abstract.php?issn=1120-6330&vol=30&iss=4&rank=8

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