= Five-mode vertical-field magnetoconvection
A <Galerkin method> approximation can retain one roll <streamfunction> mode, two temperature modes and two magnetic-flux perturbation modes in vertical-field <magnetoconvection>. Projection onto these five modes, rather than pointwise equality of the truncated fields, gives a closed system of five <ordinary differential equations>. Products generate higher spatial harmonics that are discarded by orthogonal projection. The system has symmetry $(a,b,c,d,e)\mapsto(-a,-b,c,-d,e)$ and hence admits paired steady roll branches.
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