Secondary instabilities of hexagons:a bifurcation analysis of experimentally observed Faraday wave patterns
A.M. Rucklidge, M. Silber, and J. Fineberg
Abstract. We examine three experimental observations of Faraday waves generated by two-frequency forcing, in which a primary hexagonal pattern becomes unstable to three different superlattice patterns. We use the symmetry based approach developed by Tse et al.  to analyse the bifurcations involved
in creating the three new patterns. Each of the three examples reveals a different situation that can arise in the theoretical analysis.