- 04-292 Scipio Cuccagna,Eduard Kirr, Dmitry Pelinovsky
- Parametric resonance of ground states in the nonlinear Schroedinger equation
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Sep 20, 04
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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.
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