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. 2001 Sep;64(3 Pt 2):036214.
doi: 10.1103/PhysRevE.64.036214. Epub 2001 Aug 28.

Long-wavelength instabilities of three-dimensional patterns

T K Callahan  1 , E Knobloch
Affiliations

Long-wavelength instabilities of three-dimensional patterns

T K Callahan et al. Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Sep.

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.

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