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arXiv · 0806.1183

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

Robert Conte·Svetlana Bugaychuk
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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.

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Robert Conte, Svetlana Bugaychuk. 2008-06-06. Analytic structure of the four-wave mixing model in photorefractive materials. https://doi.org/10.1142/9789812772350_0027

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