Scipio Cuccagna,Eduard Kirr, Dmitry Pelinovsky
Parametric resonance of ground states in the nonlinear Schroedinger equation
(344K, Postscript)

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 a linear 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.