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We study traveling solitary waves of the form $$ u(t,x) = e^{i\\omega t} Q_v(x-vt) $$ with frequency $\\omega \\in \\R$, velocity $v \\in \\R^d$, and some finite-energy profile $Q_v \\in H^{1/2}(\\R^d)$, $Q_v \\not \\equiv 0$. We prove that traveling solitary waves for speeds $|v| \\geq 1$ do not exist. Furthermore, we generalize the non-existence"},"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":"1808.08134","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-24T13:31:32Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"54040165a0e01ec675f749071d8491f190ff52f26491d5d20aebff42c833afca","abstract_canon_sha256":"7623b3ce3b0023b62c1f0ef87e50ee7ba4ba27eade05785aea1b02b0ee0f2e27"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:12.725996Z","signature_b64":"WyD0kUf/IiumDJluwrkuewNr5IPfNyHj8zKvxjnGr1BBzr4DHVeIDl/hvkaXzfrMRCUa8zMy6+e4fMf0UwWfDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fefc2f4da8732c72a02377593538026ba38c15f9ea6e0180f46ae6b281ed15a9","last_reissued_at":"2026-05-17T23:50:12.725543Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:12.725543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Traveling Solitary Waves and Absence of Small Data Scattering for Nonlinear Half-Wave Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Enno Lenzmann, Jacopo Bellazzini, Nicola Visciglia, Vladimir Georgiev","submitted_at":"2018-08-24T13:31:32Z","abstract_excerpt":"We consider nonlinear half-wave equations with focusing power-type nonlinearity $$ i \\pt_t u = \\sqrt{-\\Delta} \\, u - |u|^{p-1} u, \\quad \\mbox{with $(t,x) \\in \\R \\times \\R^d$} $$ with exponents $1 < p < \\infty$ for $d=1$ and $1 < p < (d+1)/(d-1)$ for $d \\geq 2$. We study traveling solitary waves of the form $$ u(t,x) = e^{i\\omega t} Q_v(x-vt) $$ with frequency $\\omega \\in \\R$, velocity $v \\in \\R^d$, and some finite-energy profile $Q_v \\in H^{1/2}(\\R^d)$, $Q_v \\not \\equiv 0$. We prove that traveling solitary waves for speeds $|v| \\geq 1$ do not exist. 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