ANALYTIC STRUCTURE OF THE FOUR-WAVE MIXING MODEL IN PHOTOREACTIVE MATERIAL

DOI10.1142/9789812772350_0027zbMATH Open1183.78029arXiv0806.1183OpenAlexW2041652432MaRDI QIDQ3400867

R. Conte, Svetlana Bugaychuk

Publication date: 5 February 2010

Published in: Waves and Stability in Continuous Media (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/0806.1183

zbMATH Keywords

Painlevé testfour-wave mixing model

Mathematics Subject Classification ID

Lasers, masers, optical bistability, nonlinear optics (78A60) Ginzburg-Landau equations (35Q56)

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