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Here $\\alpha_1$, $\\alpha_3$, $\\alpha_5$ and $c$ are such that $\\psi(x)\\equiv c$ is an energetically stable equilibrium solution to this equation. Normalizing the boundary condition to $\\psi(x)\\to 1$ as $|x|\\to\\infty$, we study the associated initial-value problem for $u=\\psi-1$ and prove a scattering result for small initial da"},"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":"1702.04413","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-14T22:52:47Z","cross_cats_sorted":[],"title_canon_sha256":"129eea85626cc7fb371569c4680f4c4755192be4a6c7816287e41d07304430d9","abstract_canon_sha256":"cd584b2a34cb8e1fb12242b91478f5fbf1441cb859bfa7c96216a0682cc96150"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:05.627353Z","signature_b64":"bDtnUWCF3EGlPDgX6Whgxjfqm2a0U/o7Z4QInZcOThIIojKfymIEjvYHpLEn9GGee+q4pJeu0c/iW5MGpDtZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9bcbd445ec10c308fe7e83d36764fe6a8d568e1ad9f6265ce7c27d6b1095d5a5","last_reissued_at":"2026-05-18T00:15:05.626862Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:05.626862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The initial-value problem for the cubic-quintic NLS with non-vanishing boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jason Murphy, Monica Visan, Rowan Killip","submitted_at":"2017-02-14T22:52:47Z","abstract_excerpt":"We consider the initial-value problem for the cubic-quintic NLS \\[ (i\\partial_t+\\Delta)\\psi=\\alpha_1 \\psi-\\alpha_{3}\\vert \\psi\\vert^2 \\psi+\\alpha_5\\vert \\psi\\vert^4 \\psi \\] in three spatial dimensions in the class of solutions with $|\\psi(x)|\\to c >0$ as $|x|\\to\\infty$. 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