 Real Ginzburg–Landau equation

The real-coefficient Ginzburg–Landau amplitude equation has complex $A$ and real parameters, usually $\xi ,g>0$ near a supercritical stationary pattern onset. A detuned plane wave $A=\rho e^{iQX}$ has ${\rho }^2=(r-\xi Q^2)/g$. Its phase and amplitude sidebands determine the narrower Eckhaus instability stability band. It is a local envelope model; additional conserved fields or mean flows may need their own equations.