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We prove the global well-posedness of this equation in $E$. Moreover, we give an explicit formula for the chiral solution to this equation."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2502.17968","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-25T08:41:50Z","cross_cats_sorted":[],"title_canon_sha256":"4d3d4a445e4ab91e045a8fb59a82b2878848f181f5038461c7447dfef7ea4e5e","abstract_canon_sha256":"6adbe47120c6336be7f8c842a71d73326a68fa214dd38e290f4dd4ddd7eb3190"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:19:47.243771Z","signature_b64":"kBTQkH8PaKPjObhJkCr9GMxc/dLwoGxUSnd0wS/Ko1F0ssGgYLKPEAGLtxX+pD9IbF5es9nvx762AoNAMiclAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"466db16ca5dd24e232ccfca6334410918c8c078cdcb77b4ada5ffbd407dd8f59","last_reissued_at":"2026-07-05T10:19:47.243376Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:19:47.243376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $E$. 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