KAM for Beating Solutions of the Quintic NLS

KAM for Beating Solutions of the Quintic NLS

We consider the nonlinear Schrödinger equation of degree five on the circle T = R / 2 π . We prove the existence of quasi-periodic solutions with four frequencies which bifurcate from “resonant” solutions [studied in Grébert and Thomann (Ann Inst Henri Poincaré Anal Non Linéaire 29(3):455–477, 2012...

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Veröffentlicht in:Communications in mathematical physics 2017-09, Vol.354 (3), p.1101-1132
Hauptverfasser: Haus, E., Procesi, M.
Format: Artikel
Sprache:eng
Schlagworte:
Bifurcations
Classical and Quantum Gravitation
Complex Systems
Fourier analysis
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Zusammenfassung:We consider the nonlinear Schrödinger equation of degree five on the circle T = R / 2 π . We prove the existence of quasi-periodic solutions with four frequencies which bifurcate from “resonant” solutions [studied in Grébert and Thomann (Ann Inst Henri Poincaré Anal Non Linéaire 29(3):455–477, 2012 )] of the system obtained by truncating the Hamiltonian after one step of Birkhoff normal form, exhibiting recurrent exchange of energy between some Fourier modes. The existence of these quasi-periodic solutions is a purely nonlinear effect.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-017-2925-7