{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:33RD4LRMY4ZXKP7Z7VFQPVBGIB","short_pith_number":"pith:33RD4LRM","schema_version":"1.0","canonical_sha256":"dee23e2e2cc733753ff9fd4b07d4264056c1c87e9e080de92a3a51f909eb6077","source":{"kind":"arxiv","id":"1408.0494","version":1},"attestation_state":"computed","paper":{"title":"A note on the existence of traveling-wave solutions to a Boussinesq system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filipe Oliveira","submitted_at":"2014-08-03T12:53:20Z","abstract_excerpt":"We obtain a one-parameter family $$(u_{\\mu}(x,t),\\eta_{\\mu}(x,t))_{\\mu\\geq \\mu_0}=(\\phi_{\\mu}(x-\\omega_{\\mu} t),\\psi_{\\mu}(x-\\omega_{\\mu} t))_{\\mu\\geq \\mu_0}$$ of traveling-wave solutions to the Boussinesq system\n  $$u_t+\\eta_x+uu_x+c\\eta_{xxx}=0,\\eta_t+u_x+(\\eta u)_x+au_{xxx}=0$$\nin the case $a,c<0$, with non-null speeds $\\omega_{\\mu}$ arbitrarily close to $0$ ($\\omega_{\\mu}\\xrightarrow[\\mu\\to+\\infty]{} 0$). We show that the $L^2$-size of such traveling-waves satisfies the uniform (in $\\mu$) estimate $\\|\\phi_{\\mu}\\|_2^2+\\|\\psi_{\\mu}\\|_2^2\\leq C\\sqrt{|a|+|c|},$ where $C$ is a positive constant"},"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":"1408.0494","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-03T12:53:20Z","cross_cats_sorted":[],"title_canon_sha256":"3d8f7e3d88687494fe91d3720f6bab6c0cf5b112783092936c393fd2ed21405d","abstract_canon_sha256":"f42e58f23f3d11278b1c8dfbaed2ee10acc2da63d26c738f25958b7a9a4901d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:56.942900Z","signature_b64":"Y6nF8kMAjQHL9C2DDp5jS2QjQw+RzvCAjOzxrUWdhsDPma4k//y32G/5eUIpwn9+TwM/dbbcMDX+WJpMDqYmCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dee23e2e2cc733753ff9fd4b07d4264056c1c87e9e080de92a3a51f909eb6077","last_reissued_at":"2026-05-18T02:45:56.942414Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:56.942414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the existence of traveling-wave solutions to a Boussinesq system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filipe Oliveira","submitted_at":"2014-08-03T12:53:20Z","abstract_excerpt":"We obtain a one-parameter family $$(u_{\\mu}(x,t),\\eta_{\\mu}(x,t))_{\\mu\\geq \\mu_0}=(\\phi_{\\mu}(x-\\omega_{\\mu} t),\\psi_{\\mu}(x-\\omega_{\\mu} t))_{\\mu\\geq \\mu_0}$$ of traveling-wave solutions to the Boussinesq system\n  $$u_t+\\eta_x+uu_x+c\\eta_{xxx}=0,\\eta_t+u_x+(\\eta u)_x+au_{xxx}=0$$\nin the case $a,c<0$, with non-null speeds $\\omega_{\\mu}$ arbitrarily close to $0$ ($\\omega_{\\mu}\\xrightarrow[\\mu\\to+\\infty]{} 0$). We show that the $L^2$-size of such traveling-waves satisfies the uniform (in $\\mu$) estimate $\\|\\phi_{\\mu}\\|_2^2+\\|\\psi_{\\mu}\\|_2^2\\leq C\\sqrt{|a|+|c|},$ where $C$ is a positive constant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0494","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1408.0494","created_at":"2026-05-18T02:45:56.942501+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.0494v1","created_at":"2026-05-18T02:45:56.942501+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.0494","created_at":"2026-05-18T02:45:56.942501+00:00"},{"alias_kind":"pith_short_12","alias_value":"33RD4LRMY4ZX","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"33RD4LRMY4ZXKP7Z","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"33RD4LRM","created_at":"2026-05-18T12:28:11.866339+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/33RD4LRMY4ZXKP7Z7VFQPVBGIB","json":"https://pith.science/pith/33RD4LRMY4ZXKP7Z7VFQPVBGIB.json","graph_json":"https://pith.science/api/pith-number/33RD4LRMY4ZXKP7Z7VFQPVBGIB/graph.json","events_json":"https://pith.science/api/pith-number/33RD4LRMY4ZXKP7Z7VFQPVBGIB/events.json","paper":"https://pith.science/paper/33RD4LRM"},"agent_actions":{"view_html":"https://pith.science/pith/33RD4LRMY4ZXKP7Z7VFQPVBGIB","download_json":"https://pith.science/pith/33RD4LRMY4ZXKP7Z7VFQPVBGIB.json","view_paper":"https://pith.science/paper/33RD4LRM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.0494&json=true","fetch_graph":"https://pith.science/api/pith-number/33RD4LRMY4ZXKP7Z7VFQPVBGIB/graph.json","fetch_events":"https://pith.science/api/pith-number/33RD4LRMY4ZXKP7Z7VFQPVBGIB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/33RD4LRMY4ZXKP7Z7VFQPVBGIB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/33RD4LRMY4ZXKP7Z7VFQPVBGIB/action/storage_attestation","attest_author":"https://pith.science/pith/33RD4LRMY4ZXKP7Z7VFQPVBGIB/action/author_attestation","sign_citation":"https://pith.science/pith/33RD4LRMY4ZXKP7Z7VFQPVBGIB/action/citation_signature","submit_replication":"https://pith.science/pith/33RD4LRMY4ZXKP7Z7VFQPVBGIB/action/replication_record"}},"created_at":"2026-05-18T02:45:56.942501+00:00","updated_at":"2026-05-18T02:45:56.942501+00:00"}