A note on growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation
Marcel Guardia
Universitat Politècnica de Catalunya, Barcelona, Spain and BGSMath Graduate School of Mathematics, Barcelona, SpainZaher Hani
University of Michigan, Ann Arbor, USAEmanuele Haus
Università die Roma Tre, ItalyAlberto Maspero
SISSA, Trieste, ItalyMichela Procesi
Università die Roma Tre, Italy
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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 topology (0 < s < 1) and whose norm can grow by any given factor.
Cite this article
Marcel Guardia, Zaher Hani, Emanuele Haus, Alberto Maspero, Michela Procesi, A note on growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 30 (2019), no. 4, pp. 865–880
DOI 10.4171/RLM/873