{"paper":{"title":"Multi-Poisson Approach to the Painlev\\'e Equations: from the Isospectral Deformation to the Isomonodromic Deformation","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Hayato Chiba","submitted_at":"2016-04-26T20:40:18Z","abstract_excerpt":"A multi-Poisson structure on a Lie algebra $\\mathfrak{g}$ provides a systematic way to construct completely integrable Hamiltonian systems on $\\mathfrak{g}$ expressed in Lax form $\\partial X_\\lambda /\\partial t = [X_\\lambda , A_\\lambda ]$ in the sense of the isospectral deformation, where $X_\\lambda , A_\\lambda \\in \\mathfrak{g}$ depend rationally on the indeterminate $\\lambda $ called the spectral parameter. In this paper, a method for modifying the isospectral deformation equation to the Lax equation $\\partial X_\\lambda /\\partial t = [X_\\lambda , A_\\lambda ] + \\partial A_\\lambda /\\partial \\la"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07847","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"}