{"paper":{"title":"Soliton resolution conjecture for the Benjamin-Ono equation: Explicit $L^\\infty$ asymptotic error formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hong-Yu Pan, Shou-Fu Tian","submitted_at":"2026-05-25T01:17:18Z","abstract_excerpt":"We prove the soliton resolution conjecture for the Benjamin-Ono (BO) equation with an explicit error bound in the $L^\\infty$-norm. For the finite-order multisoliton case, the explicit $L^\\infty$-norm errors are bounded by $\\mathcal{O}(|t|^{-\\frac{1}{4}(1-\\frac{1}{2s})})$ with initial data $u_0 \\in H^{s,\\alpha}(\\mathbb{R})$ for any $s>1/2$ and $\\alpha \\geqslant 1$. For the infinite-order multisoliton case, the explicit $L^\\infty$-norm errors are bounded by $\\mathcal{O}(|t|^{-1/3})$ when $u_0$ is expressed as an infinite sum of soliton profiles. Recently, Gassot, G\\'erard, and Miller (arXiv:2601"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25327","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25327/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"}