Light propagation in a Cole-Cole nonlinear medium via Burgers-Hopf equation

Details Light propagation in a Cole-Cole nonlinear medium via Burgers-Hopf equation Light propagation in a Cole-Cole nonlinear medium via Burgers-Hopf equation

2004-09-30

arxiv.org/abs/nlin/0409062v1

Theor. Math. Phys. vol. 144(1), pp. 968-974 (2005)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages, 4 figures, Proceedings Wokshop-Nonlinear Physics: Theory and Experiment, Gallipoli 2004

Scientific paper

10.1088/1742-5468/2004/10/P10004

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.

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