  For both cubic and quintic nonlinearities of the one-dimensional complex
Ginzburg-Landau evolution equation, we prove by a theorem of Eremenko the
finiteness of the number of traveling waves whose squared modulus has only
poles in the complex plane, and we provide all their closed form expressions.
Among these eleven solutions, five are provided by the method used. This allows
us to complete the list of solutions previously obtained by other authors.

Pattern Formation and Solitons;Fluid Dynamics;Optics