Analytic structure of the four-wave mixing model in photorefractive   materials
  In order to later find explicit analytic solutions, we investigate the singularity structure of a fundamental model of nonlinear optics, the four-wave mixing model in one space variable z. This structure is quite similar, and this is not a surprise, to that of the cubic complex Ginzburg-Landau equation. The main result is that, in order to be single valued, time-dependent solutions should depend on the space-time coordinates through the reduced variable xi=\sqrt{z} exp(-t / tau), in which tau is the relaxation time. 
Robert Conte (CEA Saclay), Svetlana Bugaychuk (Institute of physics,   Kiev)