{"paper":{"title":"On the quasi-Ablowitz-Segur and quasi-Hastings-McLeod solutions of the inhomogeneous Painlev\\'{e} II equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dan Dai, Weiying Hu","submitted_at":"2017-08-30T16:42:35Z","abstract_excerpt":"We consider the quasi-Ablowitz-Segur and quasi-Hastings-McLeod solutions of the inhomogeneous Painlev\\'e II equation $$ u\"(x)=2u^3(x)+xu(x)-\\alpha \\qquad \\textrm{for } \\alpha \\in \\mathbb{R} \\textrm{ and } |\\alpha| > \\frac{1}{2}. $$ These solutions are obtained from the classical Ablowitz-Segur and Hastings-McLeod solutions via the B\\\"acklund transformation, and satisfy the same asymptotic behaviors when $x \\to \\pm \\infty$. For $|\\alpha| > 1/2$, we show that the quasi-Ablowitz-Segur and quasi-Hastings-McLeod solutions possess $[ \\, |\\alpha| + \\frac{1}{2} \\, ]$ simple poles on the real axis, whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09357","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"}