{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:EDDFQCYFKHECFBWNZSHBVRB2SI","short_pith_number":"pith:EDDFQCYF","schema_version":"1.0","canonical_sha256":"20c6580b0551c82286cdcc8e1ac43a9210f257ca246ea0418c89b0a762a56219","source":{"kind":"arxiv","id":"1804.02222","version":1},"attestation_state":"computed","paper":{"title":"New exact superposition solutions to KdV2 equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Anna Karczewska, Piotr Rozmej","submitted_at":"2018-04-06T12:17:32Z","abstract_excerpt":"New exact solutions to the KdV2 equation (known also as the extended KdV equation) are constructed. The KdV2 equation is a second order approximation of the set of Boussinesq's equations for shallow water waves which in first order approximation yields KdV. The exact solutions ~$\\frac{A}{2}\\left(\\dn^2[B(x-vt),m]\\pm \\sqrt{m}\\,\\cn [B(x-vt),m]\\dn [B(x-vt),m]\\right)+D$~ in the form of periodic functions found in the paper complement other forms of exact solutions to KdV2 obtained earlier, i.e., the solitonic ones and periodic ones given by a single $\\cn^2$ or $\\dn^2$ Jacobi elliptic functions."},"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":"1804.02222","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-04-06T12:17:32Z","cross_cats_sorted":[],"title_canon_sha256":"267228198b3f788660b657a0df0bac94c2b77f71d6f982a05bd246da849975d0","abstract_canon_sha256":"f1d804ec1af8f4572b6f4e261912c477977eed5843819c82de02c22caf3d2063"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:05.489753Z","signature_b64":"RMjXP2L4aFZRaphqr8vX4sPKPB/Pr1jLjTHQCLHrDD97diO1aUFNlpeBN9v7bYxhxnhh4nnIQOJiQdBN3tckAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20c6580b0551c82286cdcc8e1ac43a9210f257ca246ea0418c89b0a762a56219","last_reissued_at":"2026-05-18T00:19:05.489335Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:05.489335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New exact superposition solutions to KdV2 equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Anna Karczewska, Piotr Rozmej","submitted_at":"2018-04-06T12:17:32Z","abstract_excerpt":"New exact solutions to the KdV2 equation (known also as the extended KdV equation) are constructed. The KdV2 equation is a second order approximation of the set of Boussinesq's equations for shallow water waves which in first order approximation yields KdV. The exact solutions ~$\\frac{A}{2}\\left(\\dn^2[B(x-vt),m]\\pm \\sqrt{m}\\,\\cn [B(x-vt),m]\\dn [B(x-vt),m]\\right)+D$~ in the form of periodic functions found in the paper complement other forms of exact solutions to KdV2 obtained earlier, i.e., the solitonic ones and periodic ones given by a single $\\cn^2$ or $\\dn^2$ Jacobi elliptic functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02222","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":"1804.02222","created_at":"2026-05-18T00:19:05.489394+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.02222v1","created_at":"2026-05-18T00:19:05.489394+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.02222","created_at":"2026-05-18T00:19:05.489394+00:00"},{"alias_kind":"pith_short_12","alias_value":"EDDFQCYFKHEC","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"EDDFQCYFKHECFBWN","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"EDDFQCYF","created_at":"2026-05-18T12:32:22.470017+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/EDDFQCYFKHECFBWNZSHBVRB2SI","json":"https://pith.science/pith/EDDFQCYFKHECFBWNZSHBVRB2SI.json","graph_json":"https://pith.science/api/pith-number/EDDFQCYFKHECFBWNZSHBVRB2SI/graph.json","events_json":"https://pith.science/api/pith-number/EDDFQCYFKHECFBWNZSHBVRB2SI/events.json","paper":"https://pith.science/paper/EDDFQCYF"},"agent_actions":{"view_html":"https://pith.science/pith/EDDFQCYFKHECFBWNZSHBVRB2SI","download_json":"https://pith.science/pith/EDDFQCYFKHECFBWNZSHBVRB2SI.json","view_paper":"https://pith.science/paper/EDDFQCYF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.02222&json=true","fetch_graph":"https://pith.science/api/pith-number/EDDFQCYFKHECFBWNZSHBVRB2SI/graph.json","fetch_events":"https://pith.science/api/pith-number/EDDFQCYFKHECFBWNZSHBVRB2SI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EDDFQCYFKHECFBWNZSHBVRB2SI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EDDFQCYFKHECFBWNZSHBVRB2SI/action/storage_attestation","attest_author":"https://pith.science/pith/EDDFQCYFKHECFBWNZSHBVRB2SI/action/author_attestation","sign_citation":"https://pith.science/pith/EDDFQCYFKHECFBWNZSHBVRB2SI/action/citation_signature","submit_replication":"https://pith.science/pith/EDDFQCYFKHECFBWNZSHBVRB2SI/action/replication_record"}},"created_at":"2026-05-18T00:19:05.489394+00:00","updated_at":"2026-05-18T00:19:05.489394+00:00"}