The Ginzburg–Landau equation, named after Vitaly Ginzburg and Lev Landau, describes the nonlinear evolution of small disturbances near a finite wavelength bifurcation from a stable to an unstable state of a system. At the onset of finite wavelength bifurcation, the system becomes unstable for a critical wavenumber  which is non-zero. In the neighbourhood of this bifurcation, the evolution of disturbances is characterised by the particular Fourier mode for  with slowly varying amplitude  (more precisely the real part of ). The Ginzburg–Landau equation is the governing equation for . The unstable modes can either be non-oscillatory (stationary) or oscillatory.
For non-oscillatory bifurcation,  satisfies the real Ginzburg–Landau equation
which was first derived by Alan C. Newell and John A. Whitehead and by Lee Segel in 1969. For oscillatory bifurcation,  satisfies the complex Ginzburg–Landau equation
which was first derived by Keith Stewartson and John Trevor Stuart in 1971.
When the problem is homogeneous, i.e., when  is independent of the spatial coordinates, the Ginzburg–Landau equation reduces to Stuart–Landau equation.