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.
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].
File in questo prodotto:
File Dimensione Formato  
HausProcesi.pdf

accesso aperto

Descrizione: articolo principale
Tipologia: Documento in Pre-print
Dimensione 676.92 kB
Formato Adobe PDF
676.92 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/327680
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 20
  • ???jsp.display-item.citation.isi??? 20
social impact