Stationary modulated-amplitude waves in the 1-D complex Ginzburg-Landau   equation
  We reformulate the one-dimensional complex Ginzburg-Landau equation as a fourth order ordinary differential equation in order to find stationary spatially-periodic solutions. Using this formalism, we prove the existence and stability of stationary modulated-amplitude wave solutions. Approximate analytic expressions and a comparison with numerics are given. 
Yueheng Lan, Nicolas Garnier, Predrag Cvitanovic