{"paper":{"title":"The defocusing Calogero--Moser derivative nonlinear Schr{\\\"o}dinger equation with a nonvanishing condition at infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Xi Chen (LMO)","submitted_at":"2025-02-25T08:41:50Z","abstract_excerpt":"We consider the defocusing Calogero--Moser derivative nonlinear Schr{\\\"o}dinger equation\\begin{align*}i \\partial_{t} u+\\partial_{x}^2 u-2\\Pi D\\left(|u|^{2}\\right)u=0, \\quad (t,x ) \\in \\mathbb{R} \\times \\mathbb{R}\\end{align*}posed on $E := \\left\\{u \\in L^{\\infty}(\\mathbb{R}): u' \\in  L^{2}(\\mathbb{R}), u'' \\in L^{2}(\\mathbb{R}),  |u|^{2}-1 \\in L^{2}(\\mathbb{R})\\right\\}$. We prove the global well-posedness of this equation in $E$. Moreover, we give an explicit formula for the chiral solution to this equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.17968","kind":"arxiv","version":1},"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/2502.17968/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"}