We study the nature of the nonlinear Schrödinger equation ground states on the product spaces Rn x Mk , where Mk is a compact Riemannian manifold. We prove that for small L2 masses the ground states coincide with the corresponding Rn ground states. We also prove that above a critical mass the ground states have nontrivial Mk dependence. Finally, we address the Cauchy problem issue, which transforms the variational analysis into dynamical stability results.

The nonlinear Schrödinger equation ground states on product spaces

VISCIGLIA, NICOLA
2014

Abstract

We study the nature of the nonlinear Schrödinger equation ground states on the product spaces Rn x Mk , where Mk is a compact Riemannian manifold. We prove that for small L2 masses the ground states coincide with the corresponding Rn ground states. We also prove that above a critical mass the ground states have nontrivial Mk dependence. Finally, we address the Cauchy problem issue, which transforms the variational analysis into dynamical stability results.
S., Terracini; N., Tzvetkov; Visciglia, Nicola
File in questo prodotto:
File Dimensione Formato  
Visciglia_214351.pdf

accesso aperto

Tipologia: Versione finale editoriale
Licenza: Creative commons
Dimensione 1.08 MB
Formato Adobe PDF
1.08 MB 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: http://hdl.handle.net/11568/214351
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 14
  • ???jsp.display-item.citation.isi??? 12
social impact