title: Long-wavelength instabilities of three-dimensional patterns.
abstract: Long-wavelength instabilities of steady patterns, spatially periodic in three dimensions, are studied. All potentially stable patterns with the symmetries of the simple-, face-centered- and body-centered-cubic lattices are considered. The results generalize the well-known Eckhaus, zigzag, and skew-varicose instabilities to three-dimensional patterns and are applied to two-species reaction-diffusion equations modeling the Turing instability.
authors.affiliation: Department of Physics, University of California, Berkeley, California 94720, USA. timcall@math.lsa.umich.edu
authors.forename: T K
authors.initials: TK
authors.lastname: Callahan
authors.forename: E
authors.initials: E
authors.lastname: Knobloch