Stable and unstable time quasi periodic solutions for a system of coupled NLS equations

Stable and unstable time quasi periodic solutions for a system of coupled NLS equations

We prove that a system of coupled nonlinear Schrödinger equations on the torus exhibits both stable and unstable small KAM tori. In particular, the unstable tori are related to a beating phenomena which has been proved recently in Grébert et al (2013 Nonlinearity 26 1361-76). This is the first examp...

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Veröffentlicht in:Nonlinearity 2018-10, Vol.31 (10), p.4776-4811
Hauptverfasser: Grébert, Benoît, Vilaça Da Rocha, Victor
Format: Artikel
Sprache:eng
Schlagworte:
Analysis of PDEs
Dynamical Systems
KAM theory
Mathematical Physics
Mathematics
modulational instabilities
system of coupled NLS
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Zusammenfassung:We prove that a system of coupled nonlinear Schrödinger equations on the torus exhibits both stable and unstable small KAM tori. In particular, the unstable tori are related to a beating phenomena which has been proved recently in Grébert et al (2013 Nonlinearity 26 1361-76). This is the first example of unstable tori for a 1D PDE.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/aad3d9