= Hexagonal convection amplitude equations
{title2=$A_T=\mu_2KA+\gamma K\bar B\bar C-3K^2A\sum|A_j|^2$}
A finite-<wavenumber> convection instability with a <resonant three-wave triad> can yield three coupled <amplitude equations>. For the gradient nonlinearity $\nabla\cdot(|\nabla\Theta|^2\nabla\Theta)$ and weak quadratic asymmetry $-\epsilon\gamma\nabla\cdot(\Theta\nabla\Theta)$, projection onto a triad of length squared $K$ gives the stated equation and its cyclic copies. The quadratic coefficient is $+\gamma K$, while both self and cross cubic coefficients are $-3K^2$ for angles of $120$ degrees. The finite critical mode requires positive linear damping in the underlying long-wave equation.
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