Geodesic
Light Propagation in a Cole-Cole Nonlinear Medium via the Burgers--Hopf Equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 1, pp. 102-109

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A new model of light propagation through a so-called weakly three-dimensional Cole-Cole nonlinear medium with short-range nonlocality was recently proposed. In particular, it was shown that in the geometric optics limit, the model is integrable and is governed by the dispersionless Veselov–Novikov (dVN) equation. The Burgers–Hopf equation can be obtained as a ($1+1$)-dimensional reduction of the dVN equation. We discuss its properties in the specific context of nonlinear geometric optics and consider an illustrative explicit example.
Keywords: nonlinear optics, integrable systems. 
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B. G. Konopelchenko; A. Moro. Light Propagation in a Cole-Cole Nonlinear Medium via the Burgers--Hopf Equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 1, pp. 102-109. http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a10/