A proof of the Benjamin-Feir instability
type: Item
instance of: scholarly article
title: A proof of the Benjamin-Feir instability
zbMATH Open document ID: 0845.76029
DOI: 10.1007/BF00376815
author: Thomas J. Bridges
author: Alexander Mielke
published in: Archive for Rational Mechanics and Analysis
publication date: 1996-05-22T00:00:00Z
review text: The existence and linear stability problem for the Stokes periodic wavetrain on fluids of finite depth is formulated in terms of the spatial and temporal Hamiltonian structure of the water-wave problem. A proof, within the Hamiltonian framework, of instability of the Stokes periodic wavetrain is presented. A Hamiltonian center-manifold analysis reduces the linear stability problem to an ordinary differential eigenvalue problem on \(\mathbb{R}^4\). A projection of the reduced stability problem onto the tangent space of the 2-manifold of periodic Stokes waves is used to prove the existence of a dispersion relation.
Mathematics Subject Classification ID: 76E99
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 880584
zbMATH Keywords: linear stability
zbMATH Keywords: Stokes periodic wavetrain
zbMATH Keywords: spatial and temporal Hamiltonian structure
zbMATH Keywords: center-manifold analysis
zbMATH Keywords: ordinary differential eigenvalue problem
zbMATH Keywords: dispersion relation
Wikidata QID: Q59902108
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 880584