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A simple generalization of the Swift-Hohenberg equation is proposed as amodel for the pattern-forming dynamics of a two-dimensional field with twounstable length scales. The equation is used to study the dynamics of surfacewaves in a fluid driven by a linear combination of two frequencies. The modelexhibits steady-state solutions with two-, four-, six-, and twelve-foldsymmetric patterns, similar to the periodic and quasiperiodic patterns observedin recent experiments.

Theoretical Model for Faraday Waves with Multiple-Frequency Forcing