Scattering for the nonlinear Schrödinger equation with concentrated nonlinearity
Abstract
We consider the cubic defocusing nonlinear Schrödinger equation in one dimension with the nonlinearity concentrated at a single point. We prove global well-posedness in the scaling-critical space L 2 ( R ) L^2(\mathbb {R}) and scattering for all such solutions. Moreover, we demonstrate that the same phenomenology holds whenever nonlinear effects are sufficiently concentrated in space.
Fields of Study & Subjects
Advanced Mathematical Physics Problems
Nonlinear Waves and Solitons
Nonlinear Photonic Systems
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 11
- Pages
- 4767–4780
- Publication date
- 24 April 2026
- Language
- EN