{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:FEGFELFJ3GQYWZRZEJPOOH6NLP","short_pith_number":"pith:FEGFELFJ","schema_version":"1.0","canonical_sha256":"290c522ca9d9a18b6639225ee71fcd5bf8824528f8719222e8a97e18b536937b","source":{"kind":"arxiv","id":"1810.10937","version":3},"attestation_state":"computed","paper":{"title":"Non-commutative NLS-type hierarchies: dressing & solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Anastasia Doikou, Iain Findlay, Spyridoula Sklaveniti","submitted_at":"2018-10-25T15:49:32Z","abstract_excerpt":"We consider the generalized matrix non-linear Schrodinger (NLS) hierarchy. By employing the universal Darboux-dressing scheme we derive solutions for the hierarchy of integrable PDEs via solutions of the matrix Gelfand-Levitan-Marchenko equation, and we also identify recursion relations that yield the Lax pairs for the whole matrix NLS-type hierarchy. These results are obtained considering either matrix-integral or general $n^{th}$ order matrix-differential operators as Darboux-dressing transformations. In this framework special links with the Airy and Burgers equations are also discussed. The"},"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":"1810.10937","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-10-25T15:49:32Z","cross_cats_sorted":["hep-th","math.MP","nlin.SI"],"title_canon_sha256":"85b5cce64ed7fe62f68a3e7fc9effad55dcce11bc2b19b729dfb9361a2506755","abstract_canon_sha256":"2da97aa687054102a3790bf2f3aa265c6b7df5a3885710d76353255da8254084"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:52.373222Z","signature_b64":"eiKjgPoWqiuWJ5zuMwVGTzW8OLXdID5kd2ISnAxpN4qAJ9ur9RoxHl3R9jrDaLPrt4ow5WUlUAccJtPI2UcKAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"290c522ca9d9a18b6639225ee71fcd5bf8824528f8719222e8a97e18b536937b","last_reissued_at":"2026-05-17T23:51:52.372251Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:52.372251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-commutative NLS-type hierarchies: dressing & solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Anastasia Doikou, Iain Findlay, Spyridoula Sklaveniti","submitted_at":"2018-10-25T15:49:32Z","abstract_excerpt":"We consider the generalized matrix non-linear Schrodinger (NLS) hierarchy. By employing the universal Darboux-dressing scheme we derive solutions for the hierarchy of integrable PDEs via solutions of the matrix Gelfand-Levitan-Marchenko equation, and we also identify recursion relations that yield the Lax pairs for the whole matrix NLS-type hierarchy. These results are obtained considering either matrix-integral or general $n^{th}$ order matrix-differential operators as Darboux-dressing transformations. In this framework special links with the Airy and Burgers equations are also discussed. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10937","kind":"arxiv","version":3},"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":"1810.10937","created_at":"2026-05-17T23:51:52.372379+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.10937v3","created_at":"2026-05-17T23:51:52.372379+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10937","created_at":"2026-05-17T23:51:52.372379+00:00"},{"alias_kind":"pith_short_12","alias_value":"FEGFELFJ3GQY","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"FEGFELFJ3GQYWZRZ","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"FEGFELFJ","created_at":"2026-05-18T12:32:22.470017+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/FEGFELFJ3GQYWZRZEJPOOH6NLP","json":"https://pith.science/pith/FEGFELFJ3GQYWZRZEJPOOH6NLP.json","graph_json":"https://pith.science/api/pith-number/FEGFELFJ3GQYWZRZEJPOOH6NLP/graph.json","events_json":"https://pith.science/api/pith-number/FEGFELFJ3GQYWZRZEJPOOH6NLP/events.json","paper":"https://pith.science/paper/FEGFELFJ"},"agent_actions":{"view_html":"https://pith.science/pith/FEGFELFJ3GQYWZRZEJPOOH6NLP","download_json":"https://pith.science/pith/FEGFELFJ3GQYWZRZEJPOOH6NLP.json","view_paper":"https://pith.science/paper/FEGFELFJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.10937&json=true","fetch_graph":"https://pith.science/api/pith-number/FEGFELFJ3GQYWZRZEJPOOH6NLP/graph.json","fetch_events":"https://pith.science/api/pith-number/FEGFELFJ3GQYWZRZEJPOOH6NLP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FEGFELFJ3GQYWZRZEJPOOH6NLP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FEGFELFJ3GQYWZRZEJPOOH6NLP/action/storage_attestation","attest_author":"https://pith.science/pith/FEGFELFJ3GQYWZRZEJPOOH6NLP/action/author_attestation","sign_citation":"https://pith.science/pith/FEGFELFJ3GQYWZRZEJPOOH6NLP/action/citation_signature","submit_replication":"https://pith.science/pith/FEGFELFJ3GQYWZRZEJPOOH6NLP/action/replication_record"}},"created_at":"2026-05-17T23:51:52.372379+00:00","updated_at":"2026-05-17T23:51:52.372379+00:00"}