{"paper":{"title":"On the Increasing Tritronqu\\'ee Solutions of the Painlev\\'e-II Equation","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"math.CA","authors_text":"Peter D. Miller","submitted_at":"2018-04-09T18:26:41Z","abstract_excerpt":"The increasing tritronqu\\'ee solutions of the Painlev\\'e-II equation with parameter $\\alpha$ exhibit square-root asymptotics in the maximally-large sector $|\\arg(x)|<\\tfrac{2}{3}\\pi$ and have recently appeared in applications where it is necessary to understand the behavior of these solutions for complex values of $\\alpha$. Here these solutions are investigated from the point of view of a Riemann-Hilbert representation related to the Lax pair of Jimbo and Miwa, which naturally arises in the analysis of rogue waves of infinite order. We show that for generic complex $\\alpha$, all such solutions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03173","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"}