PDE and Differential Geometry Seminar, Scattering of Schrödinger Operators with Step Potentials, by Zhiyuan Zhang (Northeastern University)
Monday, September 23, 2024 2:30–3:30 PM
- DescriptionAbstract: We consider the Schrödinger operator with a step potential. We build up a scattering and distorted Fourier transform theory for this operator, and use it to study the long-time behavior of small data solutions of the 1D cubic NLS equation with the step potential. If time permits, I will also discuss some potential application of this theory, that is, the nonlinear stability problem of dark solitons for the 1D cubic NLS equation. This is ongoing joint work with J. Holmer (Brown University).
- Websitehttps://events.uconn.edu/pde-and-differential-geometry-seminar/event/235654-pde-and-differential-geometry-seminar-scattering-of-s