报告题目：Long-time behavior for the 1d NLS with a delta potential
报告人：Prof. Jason Murphy (Missouri University of Science and Technology)
报告摘要：In this talk, I will discuss some recent joint work with S. Masaki and J. Segata. We first considered the 1d cubic NLS with a repulsive delta potential and established long-time decay and modified scattering for small initial data in a weighted Sobolev space. Next, we considered the case of an attractive delta potential with a mass-supercritical nonlinearity. In this case one has small solitary waves and does not expect small-data scattering. Instead, we prove the asymptotic stability of these small solitary waves in the energy space. That is, any small solution decouples into a sum of a small solitary wave plus a radiation part as time tends to infinity.