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.