Nonequilateral hexagonal patterns

B. A. Malomed, A. A. Nepomnyashchy, A. E. Nuz

Research output: Contribution to journalArticlepeer-review

Abstract

Rotational symmetry of pattern formation problems is the origin of a variety of patterns (rolls, squares, hexagons etc.) in convection and reaction-diffusion systems. Traditionally, only the patterns based on equilateral lattices in the Fourier space were considered. In the present paper, we develop an analysis of the patterns with slightly different lengths of the basic wave vectors. The analysis applies as well to systems with a broken rotational symmetry (convection in an inclined layer, etc.). We find, in the framework of the amplitude equations, existence and stability conditions for periodic nonequilateral patterns based on two and three wave vectors. In the latter case, special attention is paid to the case when the three amplitudes are coupled by the resonant interaction.

Original languageEnglish
Pages (from-to)357-369
Number of pages13
JournalPhysica D: Nonlinear Phenomena
Volume70
Issue number4
DOIs
StatePublished - 15 Feb 1994

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