New planforms in systems of partial differential equations with Euclidean symmetry
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.
scientific article; zbMATH DE number 832136
scientific article