Light propagation in a Cole-Cole nonlinear medium via Burgers-Hopf equation
arXiv:nlin/0409062 · doi:10.1088/1742-5468/2004/10/P10004
Abstract
Recently, a new model of propagation of the light through the so-called weakly three-dimensional Cole-Cole nonlinear medium with short-range nonlocality has been proposed. In particular, it has been shown that in the geometrical optics limit, the model is integrable and it is governed by the dispersionless Veselov-Novikov (dVN) equation. Burgers-Hopf equation can be obtained as 1+1-dimensional reduction of dVN equation. We discuss its properties in the specific context of nonlinear geometrical optics. An illustrative explicit example is considered.
10 pages, 4 figures, Proceedings Wokshop-Nonlinear Physics: Theory and Experiment, Gallipoli 2004