Scattering for the nonlinear Schrödinger equation with concentrated nonlinearity
Harrop-Griffiths B, Killip R, Vişan M. 2026. Scattering for the nonlinear Schrödinger equation with concentrated nonlinearity. Proceedings of the American Mathematical Society.
Download (ext.)
Journal Article
| Epub ahead of print
| English
Scopus indexed
Author
Harrop-Griffiths, Benjamin;
Killip, Rowan;
Vişan, MonicaISTA
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) and scattering for all such solutions. Moreover, we demonstrate that the same phenomenology holds whenever nonlinear effects are sufficiently concentrated in space.
Publishing Year
Date Published
2026-06-12
Journal Title
Proceedings of the American Mathematical Society
Publisher
American Mathematical Society
ISSN
eISSN
IST-REx-ID
Cite this
Harrop-Griffiths B, Killip R, Vişan M. Scattering for the nonlinear Schrödinger equation with concentrated nonlinearity. Proceedings of the American Mathematical Society. 2026. doi:10.1090/proc/17760
Harrop-Griffiths, B., Killip, R., & Vişan, M. (2026). Scattering for the nonlinear Schrödinger equation with concentrated nonlinearity. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/17760
Harrop-Griffiths, Benjamin, Rowan Killip, and Monica Vişan. “Scattering for the Nonlinear Schrödinger Equation with Concentrated Nonlinearity.” Proceedings of the American Mathematical Society. American Mathematical Society, 2026. https://doi.org/10.1090/proc/17760.
B. Harrop-Griffiths, R. Killip, and M. Vişan, “Scattering for the nonlinear Schrödinger equation with concentrated nonlinearity,” Proceedings of the American Mathematical Society. American Mathematical Society, 2026.
Harrop-Griffiths B, Killip R, Vişan M. 2026. Scattering for the nonlinear Schrödinger equation with concentrated nonlinearity. Proceedings of the American Mathematical Society.
Harrop-Griffiths, Benjamin, et al. “Scattering for the Nonlinear Schrödinger Equation with Concentrated Nonlinearity.” Proceedings of the American Mathematical Society, American Mathematical Society, 2026, doi:10.1090/proc/17760.
All files available under the following license(s):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]
Link(s) to Main File(s)
Access Level
Open Access
arXiv 
Google Scholar