{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:AZJMAEMIQF2EJYWGPJ24UN25HU","short_pith_number":"pith:AZJMAEMI","schema_version":"1.0","canonical_sha256":"0652c01188817444e2c67a75ca375d3d16df94a1f53f102050bf72e31b7a3540","source":{"kind":"arxiv","id":"math-ph/0702030","version":1},"attestation_state":"computed","paper":{"title":"Some explicit travelling-wave solutions of a perturbed sine-Gordon equation","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Gaetano Fiore","submitted_at":"2007-02-09T16:15:39Z","abstract_excerpt":"We present in closed form some special travelling-wave solutions (on the real line or on the circle) of a perturbed sine-Gordon equation. The perturbation of the equation consists of a constant forcing term $\\gamma$ and a linear dissipative term, and the equation is used to describe the Josephson effect in the theory of superconductors and other remarkable physical phenomena. We determine all travelling-wave solutions with unit velocity (in dimensionless units). For $|\\gamma|$ not larger than 1 we find families of solutions that are all (except the obvious constant one) manifestly unstable, wh"},"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":"math-ph/0702030","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2007-02-09T16:15:39Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"feb76f52fef90635d04a05e3b4ec3f7aecf217c3a783646b3bafe3774f27fe50","abstract_canon_sha256":"5daed56cd3b56a94aec74f0b86076542099accf30d96b6a6acf1c9f03acd349d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:34.398479Z","signature_b64":"G2lynOdKuToxtIktvmMW1FlWdSCkDirn76YBPhlyapgDBVxxqkl8JZYfmPgvd822tz12KQ4R0ERDFJryHzwbCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0652c01188817444e2c67a75ca375d3d16df94a1f53f102050bf72e31b7a3540","last_reissued_at":"2026-05-18T03:44:34.397888Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:34.397888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some explicit travelling-wave solutions of a perturbed sine-Gordon equation","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Gaetano Fiore","submitted_at":"2007-02-09T16:15:39Z","abstract_excerpt":"We present in closed form some special travelling-wave solutions (on the real line or on the circle) of a perturbed sine-Gordon equation. The perturbation of the equation consists of a constant forcing term $\\gamma$ and a linear dissipative term, and the equation is used to describe the Josephson effect in the theory of superconductors and other remarkable physical phenomena. We determine all travelling-wave solutions with unit velocity (in dimensionless units). For $|\\gamma|$ not larger than 1 we find families of solutions that are all (except the obvious constant one) manifestly unstable, wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0702030","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":"math-ph/0702030","created_at":"2026-05-18T03:44:34.397985+00:00"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0702030v1","created_at":"2026-05-18T03:44:34.397985+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0702030","created_at":"2026-05-18T03:44:34.397985+00:00"},{"alias_kind":"pith_short_12","alias_value":"AZJMAEMIQF2E","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"AZJMAEMIQF2EJYWG","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"AZJMAEMI","created_at":"2026-05-18T12:25:55.427421+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/AZJMAEMIQF2EJYWGPJ24UN25HU","json":"https://pith.science/pith/AZJMAEMIQF2EJYWGPJ24UN25HU.json","graph_json":"https://pith.science/api/pith-number/AZJMAEMIQF2EJYWGPJ24UN25HU/graph.json","events_json":"https://pith.science/api/pith-number/AZJMAEMIQF2EJYWGPJ24UN25HU/events.json","paper":"https://pith.science/paper/AZJMAEMI"},"agent_actions":{"view_html":"https://pith.science/pith/AZJMAEMIQF2EJYWGPJ24UN25HU","download_json":"https://pith.science/pith/AZJMAEMIQF2EJYWGPJ24UN25HU.json","view_paper":"https://pith.science/paper/AZJMAEMI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math-ph/0702030&json=true","fetch_graph":"https://pith.science/api/pith-number/AZJMAEMIQF2EJYWGPJ24UN25HU/graph.json","fetch_events":"https://pith.science/api/pith-number/AZJMAEMIQF2EJYWGPJ24UN25HU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AZJMAEMIQF2EJYWGPJ24UN25HU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AZJMAEMIQF2EJYWGPJ24UN25HU/action/storage_attestation","attest_author":"https://pith.science/pith/AZJMAEMIQF2EJYWGPJ24UN25HU/action/author_attestation","sign_citation":"https://pith.science/pith/AZJMAEMIQF2EJYWGPJ24UN25HU/action/citation_signature","submit_replication":"https://pith.science/pith/AZJMAEMIQF2EJYWGPJ24UN25HU/action/replication_record"}},"created_at":"2026-05-18T03:44:34.397985+00:00","updated_at":"2026-05-18T03:44:34.397985+00:00"}