{"paper":{"title":"On the Lax pairs of the sixth Painleve' equation","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Robert Conte","submitted_at":"2007-01-24T12:13:20Z","abstract_excerpt":"The dependence of the sixth equation of Painleve' on its four parameters $(2 \\alpha,-2 \\beta,2 \\gamma,1-2 \\delta) =(\\theta_{\\infty}^2,\\theta_{0}^2,\\theta_{1}^2,\\theta_{x}^2)$ is holomorphic, therefore one expects all its Lax pairs to display such a dependence. This is indeed the case of the second order scalar ``Lax'' pair of Fuchs, but the second order matrix Lax pair of Jimbo and Miwa presents a meromorphic dependence on $\\theta_\\infty$ (and a holomorphic dependence on the three other $\\theta_j$). We analyze the reason for this feature and make suggestions to suppress it."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0701049","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"}