Benjamin-Feir instability of Stokes waves
type: Item
instance of: scholarly article
title: Benjamin-Feir instability of Stokes waves
zbMATH Open document ID: 1501.35308
DOI: 10.4171/RLM/975
author: Massimiliano Berti
author: Alberto Maspero
author: P. Ventura
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2022-10-17T00:00:00Z
review text: Summary: We present the recent results in our work [Invent. Math. 230, No. 2, 651--711 (2022; Zbl 1498.76037)] regarding the Benjamin-Feir instability of small amplitude Stokes waves in deep water. We completely describe the behavior of the four eigenvalues close to zero of the linearized water waves equations at the Stokes solution, as the Floquet exponent is turned on, proving the conjecture that a pair of non-purely imaginary eigenvalues depicts a closed figure ``8'', in full agreement with numerical simulations.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 76M45
Mathematics Subject Classification ID: 70H09
Mathematics Subject Classification ID: 35S05
zbMATH DE Number: 7602453
zbMATH Keywords: traveling waves
zbMATH Keywords: modulational instability
zbMATH Keywords: Kato perturbation theory
zbMATH Keywords: water waves
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7602453