{"paper":{"title":"Long time and Painlev\\'{e}-type asymptotics for the defocusing Hirota equation with finite density initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"nlin.SI","authors_text":"Wei-Qi Peng, Yong Chen","submitted_at":"2023-07-28T03:45:02Z","abstract_excerpt":"In this work, we consider the Cauchy problem for the defocusing Hirota equation with a nonzero background \\begin{align} \\begin{cases} iq_{t}+\\alpha\\left[q_{xx}-2\\left(\\left\\vert q\\right\\vert^{2}-1\\right)q\\right]+i\\beta\\left(q_{xxx}-6\\left\\vert q\\right\\vert^{2}q_{x}\\right)=0,\\quad (x,t)\\in \\mathbb{R}\\times(0,+\\infty),\\\\ q(x,0)=q_{0}(x),\\qquad \\underset{x\\rightarrow\\pm\\infty 1}{\\lim} q_{0}(x)=\\pm 1, \\qquad q_{0}\\mp 1\\in H^{4,4}(\\mathbb{R}). \\end{cases} \\nonumber \\end{align}\n  According to the Riemann-Hilbert problem representation of the Cauchy problem and the $\\bar{\\partial}$ generalization of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.15722","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.15722/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"}