New planforms in systems of partial differential equations with Euclidean symmetry
type: Item
instance of: scholarly article
title: New planforms in systems of partial differential equations with Euclidean symmetry
zbMATH Open document ID: 0845.35010
DOI: 10.1007/BF00382886
author: I. Bosch Vivancos
author: Ian Melbourne
author: Pascal Chossat
published in: Archive for Rational Mechanics and Analysis
publication date: 1996-02-08T00:00:00Z
review text: The authors consider the classification of planforms (spatially periodic solutions corresponding to isotropy subgroups with one-dimensional fixed-point space) bifurcating in systems of partial differential equations that are equivariant with respect to the Euclidean group in the plane. A similar problem has been analyzed by Dionne and Golubitsky but in this paper, the authors consider a slightly different representation of the group, leading to three new planforms that can arise for general systems. The new planforms are called anti-rolls, simple anti-squares and simple oriented hexagons. It is shown that for general Euclidean-equivariant systems of partial differential equations there are no further axial planforms than those obtained in this paper and by Dionne and Golubitsky.
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 58E09
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 20C35
zbMATH DE Number: 832136
zbMATH Keywords: planforms
zbMATH Keywords: anti-rolls
zbMATH Keywords: simple anti-squares
zbMATH Keywords: simple oriented hexagons
zbMATH Keywords: Euclidean-equivariant systems
reviewed by: Alois Steindl
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00382886
OpenAlex ID: W2075721615
description: scientific article; zbMATH DE number 832136