We study the global existence and long-time behavior of solutions of the initial-value problem for the cubic nonlinear Schr\" odinger equation with an attractive localized potential and a time-dependent nonlinearity coefficient. For small initial data, we show under some non-degeneracy assumptions that the solution approaches the profile of the ground state and decays in time like $t^{-1/4}$. The decay is due to resonant coupling between the ground state and the radiation field induced by the time-dependent nonlinearity coefficient.

Parametric resonance of ground states in the nonlinear Schr"odinger equation

CUCCAGNA, SCIPIO;
2006-01-01

Abstract

We study the global existence and long-time behavior of solutions of the initial-value problem for the cubic nonlinear Schr\" odinger equation with an attractive localized potential and a time-dependent nonlinearity coefficient. For small initial data, we show under some non-degeneracy assumptions that the solution approaches the profile of the ground state and decays in time like $t^{-1/4}$. The decay is due to resonant coupling between the ground state and the radiation field induced by the time-dependent nonlinearity coefficient.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

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/11368/2308368
 Avviso

Registrazione in corso di verifica.
La registrazione di questo prodotto non è ancora stata validata in ArTS.

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 19
  • ???jsp.display-item.citation.isi??? ND
social impact