{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:BRUNVHHR5GOFUCJRWOFZMBENJP","short_pith_number":"pith:BRUNVHHR","schema_version":"1.0","canonical_sha256":"0c68da9cf1e99c5a0931b38b96048d4bf55022404c23b55c276a33110a3b82da","source":{"kind":"arxiv","id":"1601.02878","version":2},"attestation_state":"computed","paper":{"title":"Elliptic solutions and solitary waves of a higher order KdV--BBM long wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ronald Adams, Stefan C. Mancas","submitted_at":"2015-12-25T19:20:05Z","abstract_excerpt":"We provide conditions for existence of hyperbolic, unbounded periodic and elliptic solutions in terms of Weierstrass $\\wp$ functions of both third and fifth-order KdV--BBM (Korteweg-de Vries--Benjamin, Bona \\& Mahony) regularized long wave equation. An analysis for the initial value problem is developed together with a local and global well-posedness theory for the third-order KdV--BBM equation. Traveling wave reduction is used together with zero boundary conditions to yield solitons and periodic unbounded solutions, while for nonzero boundary conditions we find solutions in terms of Weierstra"},"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":"1601.02878","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-25T19:20:05Z","cross_cats_sorted":[],"title_canon_sha256":"eeaf84d5ab5d0ba237ad76a54f871d84b313d34969e1294b512a9c9f8a7c90f1","abstract_canon_sha256":"566cff051970fff7d76b0fe820ab1898cb7b84fd0e8d3039b895a108d6e904b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:05.612924Z","signature_b64":"e1K+hjIEZdZmCpLcACKqzTp4kp1E63jlrfa44beHOeqCzBmoS/U5pnYm+bYz2LKOLUI7kAtZmSTslwMZXtxiAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c68da9cf1e99c5a0931b38b96048d4bf55022404c23b55c276a33110a3b82da","last_reissued_at":"2026-05-18T00:31:05.612405Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:05.612405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Elliptic solutions and solitary waves of a higher order KdV--BBM long wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ronald Adams, Stefan C. Mancas","submitted_at":"2015-12-25T19:20:05Z","abstract_excerpt":"We provide conditions for existence of hyperbolic, unbounded periodic and elliptic solutions in terms of Weierstrass $\\wp$ functions of both third and fifth-order KdV--BBM (Korteweg-de Vries--Benjamin, Bona \\& Mahony) regularized long wave equation. An analysis for the initial value problem is developed together with a local and global well-posedness theory for the third-order KdV--BBM equation. Traveling wave reduction is used together with zero boundary conditions to yield solitons and periodic unbounded solutions, while for nonzero boundary conditions we find solutions in terms of Weierstra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02878","kind":"arxiv","version":2},"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":"1601.02878","created_at":"2026-05-18T00:31:05.612482+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.02878v2","created_at":"2026-05-18T00:31:05.612482+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02878","created_at":"2026-05-18T00:31:05.612482+00:00"},{"alias_kind":"pith_short_12","alias_value":"BRUNVHHR5GOF","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BRUNVHHR5GOFUCJR","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BRUNVHHR","created_at":"2026-05-18T12:29:14.074870+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/BRUNVHHR5GOFUCJRWOFZMBENJP","json":"https://pith.science/pith/BRUNVHHR5GOFUCJRWOFZMBENJP.json","graph_json":"https://pith.science/api/pith-number/BRUNVHHR5GOFUCJRWOFZMBENJP/graph.json","events_json":"https://pith.science/api/pith-number/BRUNVHHR5GOFUCJRWOFZMBENJP/events.json","paper":"https://pith.science/paper/BRUNVHHR"},"agent_actions":{"view_html":"https://pith.science/pith/BRUNVHHR5GOFUCJRWOFZMBENJP","download_json":"https://pith.science/pith/BRUNVHHR5GOFUCJRWOFZMBENJP.json","view_paper":"https://pith.science/paper/BRUNVHHR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.02878&json=true","fetch_graph":"https://pith.science/api/pith-number/BRUNVHHR5GOFUCJRWOFZMBENJP/graph.json","fetch_events":"https://pith.science/api/pith-number/BRUNVHHR5GOFUCJRWOFZMBENJP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BRUNVHHR5GOFUCJRWOFZMBENJP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BRUNVHHR5GOFUCJRWOFZMBENJP/action/storage_attestation","attest_author":"https://pith.science/pith/BRUNVHHR5GOFUCJRWOFZMBENJP/action/author_attestation","sign_citation":"https://pith.science/pith/BRUNVHHR5GOFUCJRWOFZMBENJP/action/citation_signature","submit_replication":"https://pith.science/pith/BRUNVHHR5GOFUCJRWOFZMBENJP/action/replication_record"}},"created_at":"2026-05-18T00:31:05.612482+00:00","updated_at":"2026-05-18T00:31:05.612482+00:00"}