{"paper":{"title":"Solutions of Mixed Painlev\\'e P$_{\\mathbf{III-V}}$ Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"A.H. Zimerman, H. Aratyn, J.F. Gomes, V.C.C. Alves","submitted_at":"2018-11-01T16:58:49Z","abstract_excerpt":"We review the construction of the mixed Painlev\\'e P$_{III-V}$ system in terms of a 4-boson integrable model and discuss its symmetries. Such a mixed system consist of an hybrid differential equation that for special limits of its parameters reduces to either Painlev\\'e P$_{III}$ or P$_{V}$.\n  The aim of this paper is to describe solutions of P$_{III-V}$ model. In particular, we determine and classify rational, power series and transcendental solutions of P$_{III-V}$. A class of power series solutions is shown to be convergent in accordance with the Briot-Bouquet theorem. Moreover, the P$_{III"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00495","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"}