{"paper":{"title":"Scattering of the defocusing Calogero--Moser derivative nonlinear Schr\\\"odinger equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Xi Chen","submitted_at":"2025-11-09T16:02:07Z","abstract_excerpt":"In this paper, we study the long time behavior of solutions to the defocusing Calogero--Moser derivative nonlinear Schr\\\"odinger equation (CM-DNLS). Using the G\\'erard-type explicit formula, we prove the scattering result of solutions to this equation with initial data in $H_{+}^{1,\\alpha}(\\mathbb{R}): = \\{u \\in H_{+}^1(\\mathbb{R}): |x|^{\\alpha} u \\in L^2(\\mathbb{R})\\}$ with some $\\alpha>0$. We also characterize the scattering term using the distorted Fourier transform associated with the Lax operator. This is one of the first works that apply the G\\'erard-type explicit formula to study the lo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.06432","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.06432/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}