{"paper":{"title":"Local and global well-posedness for the extended Schr\\\"{o}dinger-Benjamin-Ono system","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Justin Forlano, Puti Dai","submitted_at":"2026-06-17T16:27:25Z","abstract_excerpt":"We study the well-posedness problem for the extended Schr\\\"{o}dinger-Benjamin-Ono system (eSBO) on the real line. This system couples a Schr\\\"{o}dinger field $u$ with a Benjamin-Ono type field $v$, including a term of the form $\\partial_{x}(v^2)$. This latter term, just as in the case of the Benjamin-Ono equation, causes the system to become quasilinear and unsolvable via Picard iteration. We prove that eSBO is locally well-posed in $H^{s+\\frac 12}(\\mathbb{R})\\times H^{s}(\\mathbb{R})$ for any $s\\geq 0$. In particular, this result covers the energy space at $s=\\frac 12$, yielding global well-po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19250","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/2606.19250/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"}