= Rotational hexagon amplitude equations
For a <resonant three-wave triad> with rotational and translational <symmetry> but no spatial <reflection>, the cubic <amplitude equations> have the cyclic form $\dot A=\mu A+\overline B\,\overline C-\nu_1|A|^2A-(\nu_2+\delta)|B|^2A-(\nu_2-\delta)|C|^2A$. A half-turn induces <complex conjugation>, so all coefficients are real. The coefficient $\delta$ distinguishes the two cyclic cross-couplings that a <reflection> would interchange.
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