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Using reduction of the known Lax pair for the 3D equation, we describe nonlocal symmetries of~(1) and~(2) and show that the Lie algebras of these symmetries are isomorphic to the Witt algebra."},"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":"1707.07645","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-07-24T17:01:45Z","cross_cats_sorted":[],"title_canon_sha256":"7a9738fdfcf14ef8035683396b8d6bb598ac991725f3f7c5104b0258e8370dc6","abstract_canon_sha256":"11ad2e70e6242b72e954c1fe8d7afe51b789cdb8a0354ef0df24535771675b0e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:41.516738Z","signature_b64":"paMWRulgm3twIrfXU8nRj9HLrvjI1I8uiGOHP0/JEr8QNRJS4GsNaPgB44qYKSvqR7hObQmRAQ77W5SkC5yRAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75970dbac30ee0ba36eb4497bc9172fa37d4ef9fa3a6a703474b1ab6c5f2547c","last_reissued_at":"2026-05-18T00:39:41.516069Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:41.516069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"2D reductions of the equation $u_{yy} = u_{tx} + u_yu_{xx} - u_xu_{xy}$ and their nonlocal symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"I.S. Krasil'shchik, O.I. Morozov, P. Holba, P. Vojcak","submitted_at":"2017-07-24T17:01:45Z","abstract_excerpt":"We consider the 3D equation $u_{yy} = u_{tx} + u_yu_{xx} - u_xu_{xy}$ and its 2D reductions: (1) $u_{yy} = (u_y+y)u_{xx}-u_xu_{xy}-2$ (which is equivalent to the Gibbons-Tsarev equation) and (2) $u_{yy} = (u_y+2x)u_{xx} + (y-u_x)u_{xy} -u_x$. Using reduction of the known Lax pair for the 3D equation, we describe nonlocal symmetries of~(1) and~(2) and show that the Lie algebras of these symmetries are isomorphic to the Witt algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07645","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":"1707.07645","created_at":"2026-05-18T00:39:41.516175+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.07645v1","created_at":"2026-05-18T00:39:41.516175+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07645","created_at":"2026-05-18T00:39:41.516175+00:00"},{"alias_kind":"pith_short_12","alias_value":"OWLQ3OWDB3QL","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"OWLQ3OWDB3QLUNXL","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"OWLQ3OWD","created_at":"2026-05-18T12:31:34.259226+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/OWLQ3OWDB3QLUNXLISL3ZELS7I","json":"https://pith.science/pith/OWLQ3OWDB3QLUNXLISL3ZELS7I.json","graph_json":"https://pith.science/api/pith-number/OWLQ3OWDB3QLUNXLISL3ZELS7I/graph.json","events_json":"https://pith.science/api/pith-number/OWLQ3OWDB3QLUNXLISL3ZELS7I/events.json","paper":"https://pith.science/paper/OWLQ3OWD"},"agent_actions":{"view_html":"https://pith.science/pith/OWLQ3OWDB3QLUNXLISL3ZELS7I","download_json":"https://pith.science/pith/OWLQ3OWDB3QLUNXLISL3ZELS7I.json","view_paper":"https://pith.science/paper/OWLQ3OWD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.07645&json=true","fetch_graph":"https://pith.science/api/pith-number/OWLQ3OWDB3QLUNXLISL3ZELS7I/graph.json","fetch_events":"https://pith.science/api/pith-number/OWLQ3OWDB3QLUNXLISL3ZELS7I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OWLQ3OWDB3QLUNXLISL3ZELS7I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OWLQ3OWDB3QLUNXLISL3ZELS7I/action/storage_attestation","attest_author":"https://pith.science/pith/OWLQ3OWDB3QLUNXLISL3ZELS7I/action/author_attestation","sign_citation":"https://pith.science/pith/OWLQ3OWDB3QLUNXLISL3ZELS7I/action/citation_signature","submit_replication":"https://pith.science/pith/OWLQ3OWDB3QLUNXLISL3ZELS7I/action/replication_record"}},"created_at":"2026-05-18T00:39:41.516175+00:00","updated_at":"2026-05-18T00:39:41.516175+00:00"}