{"paper":{"title":"A symmetry reduction of the Painlev\\'{e} IV hierarchy to the Flaschka-Newell Painlev\\'{e} II hierarchy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MP","math.SG","nlin.SI"],"primary_cat":"math-ph","authors_text":"Mohamad Alameddine, Olivier Marchal","submitted_at":"2026-06-23T14:52:31Z","abstract_excerpt":"We study the isomonodromic deformation problem associated with rank-two meromorphic connections on the Riemann sphere having one regular singularity and one irregular singularity of even order at infinity, corresponding to the even Painlev\\'{e} IV hierarchy. We show that the symmetry $\\Psi(-\\lambda)= \\sigma_1 \\Psi(\\lambda) \\sigma_1$ defines an invariant submanifold whose induced isomonodromic dynamics coincides with the Flaschka-Newell Painlev\\'{e} II hierarchy. Under this identification, the corresponding Lax matrices, Darboux coordinates and Hamiltonian structures can be matched explicitly. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24662","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.24662/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}