{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FSCKGLHLJSC7NJ365BEBYJKC3S","short_pith_number":"pith:FSCKGLHL","schema_version":"1.0","canonical_sha256":"2c84a32ceb4c85f6a77ee8481c2542dc8be1330668b48efe0dff61a8fde0ad8a","source":{"kind":"arxiv","id":"1608.02324","version":1},"attestation_state":"computed","paper":{"title":"An analytic technique for the solutions of nonlinear oscillators with damping using the Abel Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"A Ghose-Choudhury, Partha Guha","submitted_at":"2016-08-08T05:44:58Z","abstract_excerpt":"Using the Chiellini condition for integrability we derive explicit solutions for a generalized system of Riccati equations $\\ddot{x}+\\alpha x^{2n+1}\\dot{x}+x^{4n+3}=0$ by reduction to the first-order Abel equation assuming the parameter $\\alpha\\ge 2\\sqrt{2(n+1)}$. The technique, which was proposed by Harko \\textit{et al}, involves use of an auxiliary system of first-order differential equations sharing a common solution with the Abel equation. In the process analytical proofs of some of the conjectures made earlier on the basis of numerical investigations in \\cite{SJKB} is provided."},"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":"1608.02324","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-08-08T05:44:58Z","cross_cats_sorted":[],"title_canon_sha256":"3057185ff14e966cc255e5c6ad9e44d835d44e6952823b48f1b939a0d4162d27","abstract_canon_sha256":"3de27d644035440f8bdcb63ead24d11c2b0b9c6358dd16ba83390f855146310d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:40.485260Z","signature_b64":"Nj3EiiIhHJxgoFutt+iQxDTc03NK0g2rDLJ4ItsoY2ZkkRIeUxXlUiajpvBuwwAwWl0mRD9UM1nQ5FKk+2pFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c84a32ceb4c85f6a77ee8481c2542dc8be1330668b48efe0dff61a8fde0ad8a","last_reissued_at":"2026-05-18T01:09:40.484843Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:40.484843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An analytic technique for the solutions of nonlinear oscillators with damping using the Abel Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"A Ghose-Choudhury, Partha Guha","submitted_at":"2016-08-08T05:44:58Z","abstract_excerpt":"Using the Chiellini condition for integrability we derive explicit solutions for a generalized system of Riccati equations $\\ddot{x}+\\alpha x^{2n+1}\\dot{x}+x^{4n+3}=0$ by reduction to the first-order Abel equation assuming the parameter $\\alpha\\ge 2\\sqrt{2(n+1)}$. The technique, which was proposed by Harko \\textit{et al}, involves use of an auxiliary system of first-order differential equations sharing a common solution with the Abel equation. In the process analytical proofs of some of the conjectures made earlier on the basis of numerical investigations in \\cite{SJKB} is provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02324","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":"1608.02324","created_at":"2026-05-18T01:09:40.484904+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.02324v1","created_at":"2026-05-18T01:09:40.484904+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02324","created_at":"2026-05-18T01:09:40.484904+00:00"},{"alias_kind":"pith_short_12","alias_value":"FSCKGLHLJSC7","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FSCKGLHLJSC7NJ36","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FSCKGLHL","created_at":"2026-05-18T12:30:15.759754+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/FSCKGLHLJSC7NJ365BEBYJKC3S","json":"https://pith.science/pith/FSCKGLHLJSC7NJ365BEBYJKC3S.json","graph_json":"https://pith.science/api/pith-number/FSCKGLHLJSC7NJ365BEBYJKC3S/graph.json","events_json":"https://pith.science/api/pith-number/FSCKGLHLJSC7NJ365BEBYJKC3S/events.json","paper":"https://pith.science/paper/FSCKGLHL"},"agent_actions":{"view_html":"https://pith.science/pith/FSCKGLHLJSC7NJ365BEBYJKC3S","download_json":"https://pith.science/pith/FSCKGLHLJSC7NJ365BEBYJKC3S.json","view_paper":"https://pith.science/paper/FSCKGLHL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.02324&json=true","fetch_graph":"https://pith.science/api/pith-number/FSCKGLHLJSC7NJ365BEBYJKC3S/graph.json","fetch_events":"https://pith.science/api/pith-number/FSCKGLHLJSC7NJ365BEBYJKC3S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FSCKGLHLJSC7NJ365BEBYJKC3S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FSCKGLHLJSC7NJ365BEBYJKC3S/action/storage_attestation","attest_author":"https://pith.science/pith/FSCKGLHLJSC7NJ365BEBYJKC3S/action/author_attestation","sign_citation":"https://pith.science/pith/FSCKGLHLJSC7NJ365BEBYJKC3S/action/citation_signature","submit_replication":"https://pith.science/pith/FSCKGLHLJSC7NJ365BEBYJKC3S/action/replication_record"}},"created_at":"2026-05-18T01:09:40.484904+00:00","updated_at":"2026-05-18T01:09:40.484904+00:00"}