---
OA_place: repository
OA_type: green
_id: '22097'
abstract:
- lang: eng
  text: 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.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Benjamin
  full_name: Harrop-Griffiths, Benjamin
  last_name: Harrop-Griffiths
- first_name: Rowan
  full_name: Killip, Rowan
  last_name: Killip
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
citation:
  ama: Harrop-Griffiths B, Killip R, Vişan M. Scattering for the nonlinear Schrödinger
    equation with concentrated nonlinearity. <i>Proceedings of the American Mathematical
    Society</i>. 2026. doi:<a href="https://doi.org/10.1090/proc/17760">10.1090/proc/17760</a>
  apa: Harrop-Griffiths, B., Killip, R., &#38; Vişan, M. (2026). Scattering for the
    nonlinear Schrödinger equation with concentrated nonlinearity. <i>Proceedings
    of the American Mathematical Society</i>. American Mathematical Society. <a href="https://doi.org/10.1090/proc/17760">https://doi.org/10.1090/proc/17760</a>
  chicago: Harrop-Griffiths, Benjamin, Rowan Killip, and Monica Vişan. “Scattering
    for the Nonlinear Schrödinger Equation with Concentrated Nonlinearity.” <i>Proceedings
    of the American Mathematical Society</i>. American Mathematical Society, 2026.
    <a href="https://doi.org/10.1090/proc/17760">https://doi.org/10.1090/proc/17760</a>.
  ieee: B. Harrop-Griffiths, R. Killip, and M. Vişan, “Scattering for the nonlinear
    Schrödinger equation with concentrated nonlinearity,” <i>Proceedings of the American
    Mathematical Society</i>. American Mathematical Society, 2026.
  ista: Harrop-Griffiths B, Killip R, Vişan M. 2026. Scattering for the nonlinear
    Schrödinger equation with concentrated nonlinearity. Proceedings of the American
    Mathematical Society.
  mla: Harrop-Griffiths, Benjamin, et al. “Scattering for the Nonlinear Schrödinger
    Equation with Concentrated Nonlinearity.” <i>Proceedings of the American Mathematical
    Society</i>, American Mathematical Society, 2026, doi:<a href="https://doi.org/10.1090/proc/17760">10.1090/proc/17760</a>.
  short: B. Harrop-Griffiths, R. Killip, M. Vişan, Proceedings of the American Mathematical
    Society (2026).
das_tickbox: '1'
date_created: 2026-06-19T08:59:17Z
date_published: 2026-06-12T00:00:00Z
date_updated: 2026-06-30T11:13:33Z
day: '12'
doi: 10.1090/proc/17760
extern: '1'
external_id:
  arxiv:
  - '2507.14571'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2507.14571
month: '06'
oa: 1
oa_version: Preprint
publication: Proceedings of the American Mathematical Society
publication_identifier:
  eissn:
  - 1088-6826
  issn:
  - 0002-9939
publication_status: epub_ahead
publisher: American Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Scattering for the nonlinear Schrödinger equation with concentrated nonlinearity
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2026'
...