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