Nonlinear Ginzburg-Landau equation
= Nonlinear Ginzburg-Landau equation
{title2=$\psi_t+U\psi_x=\mu\psi+\psi_{xx}-|\psi|^2\psi$}
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.