Nonlinear Competition between Small and Large Hexagonal Patterns

Abstract

Recent experiments by Kudrolli, Pier, and Gollub [Physica D (to be published)] on surface waves, parametrically excited by two-frequency forcing, show a transition from a small hexagonal standing wave pattern to a triangular ``superlattice`` pattern. We show that generically the hexagons and the superlattice wave patterns bifurcate simultaneously from the flat surface state as the forcing amplitude is increased, and that the experimentally observed transition can be described by considering a low-dimensional bifurcation problem. A number of predictions come out of this general analysis.