The Eckhaus instability in hexagonal patterns
type: Item
instance of: scholarly article
title: The Eckhaus instability in hexagonal patterns
zbMATH Open document ID: 0814.76044
DOI: 10.1016/0167-2789(94)90028-0
author: V. Pereyra
published in: Physica D
publication date: 1995-06-22T00:00:00Z
review text: The Eckhaus instability of hexagonal patterns is studied within the model of three coupled envelope equations for the underlying roll systems. The regions of instability in the parameter space are found analytically from both the phase approximation and a full system of amplitude equations. Beyond the stability limits of hexagons, two different modes go unstable. Both provide symmetry breaking of an initially regular pattern via splitting of a triplet of rolls into two triplets of growing disturbances. The parameters of fastest growing disturbances (wavelength, orientation, growth rate) are determined from the full set of linearized amplitude equations. The nonlinear stage of Eckhaus instability is investigated numerically.
Mathematics Subject Classification ID: 76E15
Mathematics Subject Classification ID: 76E30
zbMATH DE Number: 710195
zbMATH Keywords: coupled envelope equations
zbMATH Keywords: roll systems
zbMATH Keywords: regions of instability
zbMATH Keywords: symmetry breaking
zbMATH Keywords: linearized amplitude equations
MaRDI profile type: Publication
full work available at URL: 0167-2789(94)90028-0
OpenAlex ID: W2116193105
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description: scientific article; zbMATH DE number 710195