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

TL;DR

This paper explores light propagation in a Cole-Cole nonlinear medium using a Burgers-Hopf equation, revealing integrability in the geometrical optics limit and providing explicit examples of the model's behavior.

Contribution

It introduces a reduction of the dispersionless Veselov-Novikov equation to the Burgers-Hopf equation for modeling light in nonlinear media, highlighting its properties in geometrical optics.

Findings

Burgers-Hopf equation models light propagation in the medium.

The model is integrable in the geometrical optics limit.

An explicit example illustrates the model's application.

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.