= Quintic real Ginzburg-Landau equation
{title2=$A_T=\mu A+\alpha|A|^2A-|A|^4A+A_{XX},\quad\alpha>0$}
A cubic destabilizing term and quintic saturation describe a subcritical stationary pattern bifurcation. A plane wave $A=Re^{iQX}$ has squared amplitude $x=R^2$ satisfying $\mu-Q^2+\alpha x-x^2=0$. The nonzero branches meet at $x=\alpha/2$, $\mu=Q^2-\alpha^2/4$. The lower branch is unstable to amplitude perturbations; the upper branch can also undergo an <Eckhaus instability> of its phase.
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