Three coupled Ginzburg-Landau equations for hexagonal patterns with broken
chiral symmetry are investigated. They are relevant for the dynamics close to
onset of rotating non-Boussinesq or surface-tension-driven convection. Steady
and oscillatory, long- and short-wave instabilities of the hexagons are found.
For the long-wave behavior coupled phase equations are derived. Numerical
simulations of the Ginzburg-Landau equations indicate bistability between
spatio-temporally chaotic patterns and stable steady hexagons. The chaotic
state can, however, not be described properly with the Ginzburg-Landau
equations.Comment: 11 pages, 7 figures, submitted to Physica