{"paper":{"title":"Two-component soliton systems and the Painlev\\'e equations","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Mikio Murata","submitted_at":"2006-03-31T23:48:09Z","abstract_excerpt":"We give an extension of the two-component KP hierarchy by considering additional time variables. We obtain the linear $2\\times 2$ system by taking into consideration the hierarchy through a reduction procedure. The Lax pair of the Schlesinger system and the sixth Painlev\\'e equation is given from this linear system. A unified approach to treat the other Painlev\\'e equations from the usual two-component KP hierarchy is also considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0604001","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"}