Analytic structure of the four-wave mixing model in photorefractive materials

Abstract

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.

5 pages, Waves and stability in continuous media, 30 June-7 July 2007, Scicli (Rg), Italy