Nonlinear Competition Between Small and Large Hexagonal Patterns

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  • 8 October 1997
Abstract
Recent experiments by Kudrolli, Pier and Gollub on surface waves, parametrically excited by two-frequency forcing, show a transition from a small hexagonal standing wave pattern to a large triangular superlattice pattern. We show that generically the small hexagonal and the large triangular 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 degenerate bifurcation problem. In particular, the transition from the small hexagonal pattern to the triangular superlattice pattern can be favored over the ubiquitous hexagons-to-rolls transition.

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