{"scopus_import":"1","external_id":{"arxiv":["2207.02414"]},"OA_type":"green","author":[{"first_name":"Rowan","last_name":"Killip","full_name":"Killip, Rowan"},{"full_name":"Murphy, Jason","last_name":"Murphy","first_name":"Jason"},{"id":"056daca0-b8d1-11f0-964f-f91054abf8ca","first_name":"Monica","last_name":"Visan","full_name":"Visan, Monica"}],"issue":"6","type":"journal_article","article_processing_charge":"No","oa":1,"citation":{"ieee":"R. Killip, J. Murphy, and M. Vişan, “The scattering map determines the nonlinearity,” <i>Proceedings of the American Mathematical Society</i>, vol. 151, no. 6. American Mathematical Society, pp. 2543–2557, 2023.","ista":"Killip R, Murphy J, Vişan M. 2023. The scattering map determines the nonlinearity. Proceedings of the American Mathematical Society. 151(6), 2543–2557.","apa":"Killip, R., Murphy, J., &#38; Vişan, M. (2023). The scattering map determines the nonlinearity. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/proc/16297\">https://doi.org/10.1090/proc/16297</a>","mla":"Killip, Rowan, et al. “The Scattering Map Determines the Nonlinearity.” <i>Proceedings of the American Mathematical Society</i>, vol. 151, no. 6, American Mathematical Society, 2023, pp. 2543–57, doi:<a href=\"https://doi.org/10.1090/proc/16297\">10.1090/proc/16297</a>.","chicago":"Killip, Rowan, Jason Murphy, and Monica Vişan. “The Scattering Map Determines the Nonlinearity.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2023. <a href=\"https://doi.org/10.1090/proc/16297\">https://doi.org/10.1090/proc/16297</a>.","short":"R. Killip, J. Murphy, M. Vişan, Proceedings of the American Mathematical Society 151 (2023) 2543–2557.","ama":"Killip R, Murphy J, Vişan M. The scattering map determines the nonlinearity. <i>Proceedings of the American Mathematical Society</i>. 2023;151(6):2543-2557. doi:<a href=\"https://doi.org/10.1090/proc/16297\">10.1090/proc/16297</a>"},"day":"01","OA_place":"repository","das_tickbox":"1","intvolume":"       151","publisher":"American Mathematical Society","article_type":"original","date_created":"2026-06-19T08:12:42Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","publication_identifier":{"eissn":["1088-6826"],"issn":["0002-9939"]},"doi":"10.1090/proc/16297","extern":"1","publication":"Proceedings of the American Mathematical Society","abstract":[{"text":"Using the two-dimensional nonlinear Schrödinger equation as a model example, we present a general method for recovering the nonlinearity of a nonlinear dispersive equation from its small-data scattering behavior. We prove that under very mild assumptions on the nonlinearity, the wave operator uniquely determines the nonlinearity, as does the scattering map. Evaluating the scattering map on well-chosen initial data, we reduce the problem to an inverse convolution problem, which we solve by means of an application of the Beurling–Lax Theorem.","lang":"eng"}],"publication_status":"published","title":"The scattering map determines the nonlinearity","volume":151,"arxiv":1,"page":"2543-2557","status":"public","mathsc":["35Q55"],"month":"06","year":"2023","date_updated":"2026-06-30T07:08:20Z","language":[{"iso":"eng"}],"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2207.02414"}],"_id":"22064","date_published":"2023-06-01T00:00:00Z"}