The CGLE marries several key concepts which were developed in the years before the CGLE became well-known, particularly in the context of pattern formation. Thus, we first review the origins of these concepts before giving the first uses of the RGLE and CGLE.
Landau (1944) was the first to make use of slow relaxation times in an investigation into turbulence. (This was also one of the earliest uses of a weakly nonlinear expansion.) In relation to pattern formation, this approach was introduced by Stuart (1969). Landau (1937) was also the first to propose slow spatial dependence in the context of x-ray scattering by crystals. However, the concept became well-known through the success of his collaboration with Ginzburg (Ginzburg and Landau, 1950) which spawned the so-called Ginzburg-Landau theory for superconductivity.
Real Ginzburg-Landau equations were first derived as long-wave amplitude equations by Newell and Whitehead (1969) and Segel (1969) in the context of convection in binary mixtures near the onset of instability. Complex Ginzburg-Landau equations were first derived by Stewartson and Stuart (1971) who studied Poiseuille flow, and by Ermentrout (1981) through the investigation of reaction-diffusion systems.