= Periodic stability criterion for a conserved-field uniform amplitude
{title2=$r>0,\quad (\pi/L)^2+r-2\delta R^2>0,\quad r=R(2R-\alpha)$}
A nonzero uniform <equilibrium> of the <conserved-field real amplitude equation> obeys $\mu=R^2-\alpha R$. Fixed zero mean excludes the constant $B$ perturbation. Its homogeneous amplitude <eigenvalue> is $-r$. For a nonzero Fourier <wavenumber> $k$, the <stability matrix> has <trace> $-r-(1+\sigma)k^2$ and <determinant> $\sigma k^2(k^2+r-2\delta R^2)$. The displayed conditions are necessary and sufficient for strict <linear stability> on a period $2L$. In an infinite-domain limit the nonzero-mode condition becomes $r\geq2\delta R^2$; a long-wave instability need not occur in a sufficiently short domain.
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