{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:UBCBJEOA57JWK5D6FUKC23W2OZ","short_pith_number":"pith:UBCBJEOA","schema_version":"1.0","canonical_sha256":"a0441491c0efd365747e2d142d6eda765c99541ae1aae33db8bba569e68c50e1","source":{"kind":"arxiv","id":"1908.03873","version":1},"attestation_state":"computed","paper":{"title":"Discontinuous Galerkin methods for the Ostrovsky-Vakhnenko equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Qian Zhang, Yinhua Xia","submitted_at":"2019-08-11T08:50:19Z","abstract_excerpt":"In this paper, we develop discontinuous Galerkin (DG) methods for the Ostrovsky-Vakhnenko (OV) equation, which yields the shock solutions and singular soliton solutions, such as peakon, cuspon and loop solitons. The OV equation has also been shown to have a bi-Hamiltonian structure. We directly develop the energy stable or Hamiltonian conservative discontinuous Galerkin (DG) schemes for the OV equation. Error estimates for the two energy stable schemes are also proved. For some singular solutions, including cuspon and loop soliton solutions, the hodograph transformation is adopted to transform"},"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":"1908.03873","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-11T08:50:19Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"2e8f55ce4c1aa5d41d6d0903b65dbd8b7093455921bd9acade0c6fa3be0382c7","abstract_canon_sha256":"2b6617c71314e873e089ea9a57ea5dd8fa2175c186abfe4a4319333bb4139c77"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:53:19.079383Z","signature_b64":"vKI8DrnPP5Dpc+dN3WknM/bvYPzRoRkU7WT2Oh1GQ51L2Qhw/oxqa0Sx43ecgrhvTgDUKBYpyUSA59XWnKZUDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0441491c0efd365747e2d142d6eda765c99541ae1aae33db8bba569e68c50e1","last_reissued_at":"2026-07-04T23:53:19.079022Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:53:19.079022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Discontinuous Galerkin methods for the Ostrovsky-Vakhnenko equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Qian Zhang, Yinhua Xia","submitted_at":"2019-08-11T08:50:19Z","abstract_excerpt":"In this paper, we develop discontinuous Galerkin (DG) methods for the Ostrovsky-Vakhnenko (OV) equation, which yields the shock solutions and singular soliton solutions, such as peakon, cuspon and loop solitons. The OV equation has also been shown to have a bi-Hamiltonian structure. We directly develop the energy stable or Hamiltonian conservative discontinuous Galerkin (DG) schemes for the OV equation. Error estimates for the two energy stable schemes are also proved. For some singular solutions, including cuspon and loop soliton solutions, the hodograph transformation is adopted to transform"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03873","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.03873/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.03873","created_at":"2026-07-04T23:53:19.079077+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.03873v1","created_at":"2026-07-04T23:53:19.079077+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03873","created_at":"2026-07-04T23:53:19.079077+00:00"},{"alias_kind":"pith_short_12","alias_value":"UBCBJEOA57JW","created_at":"2026-07-04T23:53:19.079077+00:00"},{"alias_kind":"pith_short_16","alias_value":"UBCBJEOA57JWK5D6","created_at":"2026-07-04T23:53:19.079077+00:00"},{"alias_kind":"pith_short_8","alias_value":"UBCBJEOA","created_at":"2026-07-04T23:53:19.079077+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/UBCBJEOA57JWK5D6FUKC23W2OZ","json":"https://pith.science/pith/UBCBJEOA57JWK5D6FUKC23W2OZ.json","graph_json":"https://pith.science/api/pith-number/UBCBJEOA57JWK5D6FUKC23W2OZ/graph.json","events_json":"https://pith.science/api/pith-number/UBCBJEOA57JWK5D6FUKC23W2OZ/events.json","paper":"https://pith.science/paper/UBCBJEOA"},"agent_actions":{"view_html":"https://pith.science/pith/UBCBJEOA57JWK5D6FUKC23W2OZ","download_json":"https://pith.science/pith/UBCBJEOA57JWK5D6FUKC23W2OZ.json","view_paper":"https://pith.science/paper/UBCBJEOA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.03873&json=true","fetch_graph":"https://pith.science/api/pith-number/UBCBJEOA57JWK5D6FUKC23W2OZ/graph.json","fetch_events":"https://pith.science/api/pith-number/UBCBJEOA57JWK5D6FUKC23W2OZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UBCBJEOA57JWK5D6FUKC23W2OZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UBCBJEOA57JWK5D6FUKC23W2OZ/action/storage_attestation","attest_author":"https://pith.science/pith/UBCBJEOA57JWK5D6FUKC23W2OZ/action/author_attestation","sign_citation":"https://pith.science/pith/UBCBJEOA57JWK5D6FUKC23W2OZ/action/citation_signature","submit_replication":"https://pith.science/pith/UBCBJEOA57JWK5D6FUKC23W2OZ/action/replication_record"}},"created_at":"2026-07-04T23:53:19.079077+00:00","updated_at":"2026-07-04T23:53:19.079077+00:00"}