{"paper":{"title":"On higher order isolas of unstable Stokes waves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alberto Maspero, Livia Corsi, Massimiliano Berti, Paolo Ventura","submitted_at":"2025-01-02T18:06:21Z","abstract_excerpt":"We overview the recent result [3, Theorem 1.1] about the high-frequency instability of Stokes waves subject to longitudinal perturbations. The spectral bands of unstable eigenvalues away from the origin form a sequence of {\\it isolas} parameterized by an integer $ \\mathtt{p} \\geq 2 $ for any value of the depth $ \\mathtt{h} > 0 $ such that an explicit analytic function $\\beta_1^{(\\mathtt{p})}(\\mathtt{h}) $ is not zero. In [3] it is proved that the map $ \\mathtt{h} \\mapsto \\beta_1^{(\\mathtt{p})}(\\mathtt{h}) $ is not identically zero for any $ \\mathtt{p} \\geq 2 $ by showing that $ \\lim_{\\mathtt{h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.01390","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/2501.01390/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"}