{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:BPJXM3P4UHXKPRWYG4AQPO2ADH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"91c5b3554b2b7db55d90392cd91875628620bc644c23d64c8a2cd61c977a1977","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-09-10T19:31:57Z","title_canon_sha256":"e9315bee26739c35697adc03f5b6c459191064c52caada1c39f7bb46a24c7d2f"},"schema_version":"1.0","source":{"id":"0909.2020","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.2020","created_at":"2026-05-18T02:40:04Z"},{"alias_kind":"arxiv_version","alias_value":"0909.2020v2","created_at":"2026-05-18T02:40:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.2020","created_at":"2026-05-18T02:40:04Z"},{"alias_kind":"pith_short_12","alias_value":"BPJXM3P4UHXK","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BPJXM3P4UHXKPRWY","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BPJXM3P4","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:e237d0803074b0628fb1488ea9e13abbab908123e32a1473221b9f7181d25be5","target":"graph","created_at":"2026-05-18T02:40:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Studied here is the generalized Benjamin-Ono--Zakharov-Kuznetsov equation $u_t+u^pu_x+\\alpha\\mathscr{H}u_{xx}+\\varepsilon u_{xyy}=0, \\quad (x,y)\\in\\rr^2\\!,\\;\\;t\\in \\rr^+\\!$ in two space dimensions. Here, $\\mathscr{H}$ is the Hilbert transform and subscripts denote partial differentiation. We classify when equation (1) possesses solitary-wave solutions in terms of the signs of the constants $\\alpha$ and $\\varepsilon$ appearing in the dispersive terms and the strength of the nonlinearity. Regularity and decay properties of these solitary wave are determined and their stability is studied.","authors_text":"Ademir Pastor, Amin Esfahani, Jerry L. Bona","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-09-10T19:31:57Z","title":"Stability and Decay properties of Solitary wave solutions for the generalized BO-ZK equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.2020","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:257e6f1f662d1b20c6ce50a5b88142ca0a5f6b47db66cc869a1d2aef74c2bc27","target":"record","created_at":"2026-05-18T02:40:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"91c5b3554b2b7db55d90392cd91875628620bc644c23d64c8a2cd61c977a1977","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-09-10T19:31:57Z","title_canon_sha256":"e9315bee26739c35697adc03f5b6c459191064c52caada1c39f7bb46a24c7d2f"},"schema_version":"1.0","source":{"id":"0909.2020","kind":"arxiv","version":2}},"canonical_sha256":"0bd3766dfca1eea7c6d8370107bb4019dd8b05a040af70a8871cff80107e03e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bd3766dfca1eea7c6d8370107bb4019dd8b05a040af70a8871cff80107e03e7","first_computed_at":"2026-05-18T02:40:04.154625Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:04.154625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bizWd1OOED5AltrP2HBW6TljoqSmwO54FL6BlesvGgwvuyGFfSYLaJseWwotfALvDHVjt6EBJCexAXGm0BgBCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:04.155155Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.2020","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:257e6f1f662d1b20c6ce50a5b88142ca0a5f6b47db66cc869a1d2aef74c2bc27","sha256:e237d0803074b0628fb1488ea9e13abbab908123e32a1473221b9f7181d25be5"],"state_sha256":"5e583adef3b71524bbf64ce74dad70ea7de6809f4ec2382f081e417820064906"}