We 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. - 220:1(2006), pp. 85-120. [10.1016/j.jde.2005.07.009]
Parametric resonance of ground states in the nonlinear Schr"odinger equation
CUCCAGNA, Scipio;
2006
Abstract
We 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.Pubblicazioni consigliate
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