{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-higher-order-isolas-of-unstable-stokes","title":"On higher order isolas of unstable Stokes waves","arxiv_id":"2501.01390","date":"2025-01-02","proceeding":null,"authors":["Massimiliano Berti","Livia Corsi","Alberto Maspero","Paolo Ventura"],"abstract":"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} \\to 0^+}\\beta_1^{(\\mathtt{p})}(\\mathtt{h}) = - \\infty $. In this manuscript we compute the asymptotic expansion of $\\beta_1^{(\\mathtt{p})}(\\mathtt{h}) $ in the deep-water limit $ \\mathtt{h} \\to + \\infty $ -- it vanishes exponentially fast to zero -- for $\\mathtt{p}=2$, $3$, $4$.","url_abs":"https://arxiv.org/abs/2501.01390v1","url_pdf":"https://arxiv.org/pdf/2501.01390v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"on-higher-order-isolas-of-unstable-stokes","repo_url":"https://git-scm.sissa.it/amaspero/on-higher-order-isolas-of-unstable-stokes-waves","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}