We consider the nonlinear Schrödinger equation of degree five on the circle T= R/ 2 Ï. We prove the existence of quasi-periodic solutions with four frequencies which bifurcate from âresonantâ solutions [studied in Grébert and Thomann (Ann Inst Henri Poincaré Anal Non Linéaire 29(3):455â477, 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 Ï. We prove the existence of quasi-periodic solutions with four frequencies which bifurcate from âresonantâ solutions [studied in Grébert and Thomann (Ann Inst Henri Poincaré Anal Non Linéaire 29(3):455â477, 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.| File | Dimensione | Formato | |
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