- 15-66 Riccardo Adami, Diego Noja, Cecilia Ortoleva
- Asymptotic stability for standing waves of a NLS equation with concentrated nonlinearity in dimension three. II
Jul 17, 15
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Abstract. We investigate the asymptotic stability of standing waves for a model of Schroedinger equation with spatially concentrated nonlinearity in space dimension three. The nonlinearity studied is a power nonlinearity concentrated at the point x=0, obtained by considering a contact (or δ) interaction with a strength depending on the wavefunction in a prescribed way. Without using the Fermi Golden Rule we prove that, in a certain range of the nonlinearity power, the dynamics near the orbit of a standing wave asymptotically relaxes towards a standing state. Contrarily to the main results in the field, the admitted nonlinearity is L2-subcritical.