Spectral stability of wave trains in the Kawahara equation
type: Item
instance of: scholarly article
title: Spectral stability of wave trains in the Kawahara equation
zbMATH Open document ID: 1111.35060
author: Mariana Haragus
author: Eric Lombardi
author: Arnd Scheel
published in: Journal of Mathematical Fluid Mechanics
publication date: 2007-02-14T00:00:00Z
review text: The authors consider the Kawahara equation \[ \partial_t u= \partial^5_x u- \varepsilon\partial^3_x u+ u\partial_x u,\tag{1} \] where \(\varepsilon\) is a real parameter. The goal of the authors is to study the spectral stability of the periodic wave trains at the tail of the generalized solitary waves of (1), with respect to localized bounded perturbations. They prove that periodic travelling waves with speed \(c\) are spectrally stable, that is, the spectrum of the linearization about these waves is contained in the imaginary axis, provided their amplitude \(A\) satisfies \(A= o(|c|^{5/4})\).
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 37K45
zbMATH DE Number: 5126600
zbMATH Keywords: periodic solutions
zbMATH Keywords: stability
zbMATH Keywords: dispersive equations
MaRDI profile type: Publication
full work available at URL: s00021-005-0185-3
OpenAlex ID: W2136607425
DOI: 10.1007/S00021-005-0185-3
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description: scientific article; zbMATH DE number 5126600