{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:DTMOLIKH5RR5EV3ZJULHUCVKM2","short_pith_number":"pith:DTMOLIKH","schema_version":"1.0","canonical_sha256":"1cd8e5a147ec63d257794d167a0aaa669c919d240dd3e82dcb54b70a5f48417d","source":{"kind":"arxiv","id":"1304.1703","version":2},"attestation_state":"computed","paper":{"title":"Modified Korteweg-de Vries equation: modulated elliptic wave and a train of asymptotic solitons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Minakov Alexander, Vladimir Kotlyarov","submitted_at":"2013-04-05T13:21:08Z","abstract_excerpt":"We study the long-time asymptotic behavior of the Cauchy problem for the modified Korteweg - de Vries equation with an initial function of the step type. This function rapidly tends to zero as $x\\to+\\infty$ and to some positive constant c as $x\\to-\\infty$. In 1989 E. Khruslov and V. Kotlyarov have found that for a large time the solution breaks up into a train of asymptotic solitons located in the domain $4c^2t-C_N \\ln t<x\\leq4c^2t$ ($C_N$ is a constant). The number N of these solitons grows unboundedly as $t\\to\\infty$. In 2010 V. Kotlyarov and A. Minakov have studied temporary asymptotics of "},"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":"1304.1703","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-05T13:21:08Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"71477739b2e3efad0435abe06de9a90c5015eb22c9f11b032dc03d567a1bea0f","abstract_canon_sha256":"59c81bc8935d86932efc8b11ba697da92ca7ff873439adaca727b4ebc9cc0451"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:12.583083Z","signature_b64":"YwrMxZi7Ruuo9ciaQhPrpKY69X8zq47Gz+3m5u0gNXCNHPuJKAqmKC0BAVHTfjFFtVzoYQJbUUKaagFW825XAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cd8e5a147ec63d257794d167a0aaa669c919d240dd3e82dcb54b70a5f48417d","last_reissued_at":"2026-05-18T02:17:12.582383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:12.582383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modified Korteweg-de Vries equation: modulated elliptic wave and a train of asymptotic solitons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Minakov Alexander, Vladimir Kotlyarov","submitted_at":"2013-04-05T13:21:08Z","abstract_excerpt":"We study the long-time asymptotic behavior of the Cauchy problem for the modified Korteweg - de Vries equation with an initial function of the step type. This function rapidly tends to zero as $x\\to+\\infty$ and to some positive constant c as $x\\to-\\infty$. In 1989 E. Khruslov and V. Kotlyarov have found that for a large time the solution breaks up into a train of asymptotic solitons located in the domain $4c^2t-C_N \\ln t<x\\leq4c^2t$ ($C_N$ is a constant). The number N of these solitons grows unboundedly as $t\\to\\infty$. In 2010 V. Kotlyarov and A. Minakov have studied temporary asymptotics of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1703","kind":"arxiv","version":2},"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":"1304.1703","created_at":"2026-05-18T02:17:12.582496+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.1703v2","created_at":"2026-05-18T02:17:12.582496+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1703","created_at":"2026-05-18T02:17:12.582496+00:00"},{"alias_kind":"pith_short_12","alias_value":"DTMOLIKH5RR5","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"DTMOLIKH5RR5EV3Z","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"DTMOLIKH","created_at":"2026-05-18T12:27:43.054852+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/DTMOLIKH5RR5EV3ZJULHUCVKM2","json":"https://pith.science/pith/DTMOLIKH5RR5EV3ZJULHUCVKM2.json","graph_json":"https://pith.science/api/pith-number/DTMOLIKH5RR5EV3ZJULHUCVKM2/graph.json","events_json":"https://pith.science/api/pith-number/DTMOLIKH5RR5EV3ZJULHUCVKM2/events.json","paper":"https://pith.science/paper/DTMOLIKH"},"agent_actions":{"view_html":"https://pith.science/pith/DTMOLIKH5RR5EV3ZJULHUCVKM2","download_json":"https://pith.science/pith/DTMOLIKH5RR5EV3ZJULHUCVKM2.json","view_paper":"https://pith.science/paper/DTMOLIKH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.1703&json=true","fetch_graph":"https://pith.science/api/pith-number/DTMOLIKH5RR5EV3ZJULHUCVKM2/graph.json","fetch_events":"https://pith.science/api/pith-number/DTMOLIKH5RR5EV3ZJULHUCVKM2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DTMOLIKH5RR5EV3ZJULHUCVKM2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DTMOLIKH5RR5EV3ZJULHUCVKM2/action/storage_attestation","attest_author":"https://pith.science/pith/DTMOLIKH5RR5EV3ZJULHUCVKM2/action/author_attestation","sign_citation":"https://pith.science/pith/DTMOLIKH5RR5EV3ZJULHUCVKM2/action/citation_signature","submit_replication":"https://pith.science/pith/DTMOLIKH5RR5EV3ZJULHUCVKM2/action/replication_record"}},"created_at":"2026-05-18T02:17:12.582496+00:00","updated_at":"2026-05-18T02:17:12.582496+00:00"}