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.

Haus, E., Procesi, M. (2017). KAM for Beating Solutions of the Quintic NLS. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 354(3), 1101-1132 [10.1007/s00220-017-2925-7].

KAM for Beating Solutions of the Quintic NLS

Haus, E.
;
Procesi, M.
2017-01-01

Abstract

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.
2017
Haus, E., Procesi, M. (2017). KAM for Beating Solutions of the Quintic NLS. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 354(3), 1101-1132 [10.1007/s00220-017-2925-7].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/327680
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