{"paper":{"title":"Connection problem for the tau-function of the Sine-Gordon reduction of Painlev\\'{e}-III equation via the Riemann-Hilbert approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Alexander Its, Andrei Prokhorov","submitted_at":"2015-06-24T18:03:45Z","abstract_excerpt":"We evaluate explicitly, in terms of the Cauchy data, the constant pre-factor in the large $x$ asymptotics of the Painlev\\'e III tau-function. Our result proves the conjectural formula for this pre-factor obtained recently by O. Lisovyy, Y. Tykhyy, and the first co-author with the help of the recently discovered connection of the Painlev\\'e tau-functions with the Virasoro conformal blocks. Our approach does not use this connection, and it is based on the Riemann-Hilbert method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07485","kind":"arxiv","version":4},"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"}