 Nonlinear Ginzburg-Landau equation

This nondispersive cubic complex Ginzburg–Landau equation balances linear growth against nonlinear damping. Its real-wavenumber Ginzburg-Landau plane wave has amplitude $\sqrt{\mu -k^2}$ when $\mu >k^2$. Relaxation within that single-mode amplitude family does not by itself establish stability against general perturbations.