S. Cuccagna, E. Kirr, and D. Pelinovsky

Parametric resonance of ground states in the nonlinear Schrodinger equation

J. Diff. Eqs. 220, 85-120 (2006)

Abstract:
We study the global existence and long-time behavior of solutions of the initial-value problem for the cubic nonlinear Schrodinger 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.

Keywords:
SPECTRAL THEORY, NONLINEAR SCHRODINGER EQUATION, BOUND STATES, PARAMETRIC RESONANCE, FERMI GOLDEN RULE, RADIATIVE DECAY