EnglishWe study the global existence and long-time behavior of solutions ofthe initial-value problem for the cubic nonlinear Schr\" odingerequation with an attractive localized potential and a time-dependentnonlinearity coefficient. For small initial data, we show under somenon-degeneracy assumptions that the solution approaches the profileof the ground state and decays in time like $t^{-1/4}$. The decay isdue to resonant coupling between the ground state and the radiationfield induced by the time-dependent nonlinearity coefficient.
Parametric resonance of ground states in the nonlinear Schr"odinger equation / Cuccagna, Scipio; Eduard, Kirr; Dmitry, Pelinovsky. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 220(2006), pp. 85-120.
| Data di pubblicazione: | 2006 | |
| Titolo: | Parametric resonance of ground states in the nonlinear Schr"odinger equation | |
| Autore/i: | Cuccagna, Scipio; Eduard, Kirr; Dmitry, Pelinovsky | |
| Autore/i UNIMORE: | ||
| Rivista: | ||
| Volume: | 220 | |
| Pagina iniziale: | 85 | |
| Pagina finale: | 120 | |
| Codice identificativo ISI: | WOS:000233889300005 | |
| Codice identificativo Scopus: | 2-s2.0-28344456247 | |
| Citazione: | Parametric resonance of ground states in the nonlinear Schr"odinger equation / Cuccagna, Scipio; Eduard, Kirr; Dmitry, Pelinovsky. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 220(2006), pp. 85-120. | |
| Tipologia | Articolo su rivista |
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