= Travelling and standing convection rolls
= Traveling and standing convection rolls
{synonym}
At fixed orientation, opposite travelling amplitudes can obey $\dot Z_\pm=(r+i\omega_0)Z_\pm-(g|Z_\pm|^2+h|Z_\mp|^2)Z_\pm$. For $r>0$ and $g_r=\operatorname{Re}g>0$, a travelling branch has one nonzero intensity $r/g_r$ and is stable to its counter-propagating amplitude when $h_r>g_r$. A standing branch has both intensities $r/(g_r+h_r)$ and is stable within the pair when $g_r>h_r$ and $g_r+h_r>0$. These follow by linearizing the real intensity equations. Spatial modulation and other orientations remain separate stability tests.
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