Integrable equations in nonlinear geometrical optics
可精确求解与可积系统
2012-10-01 v1 经典物理
摘要
Geometrical optics limit of the Maxwell equations for nonlinear media with the Cole-Cole dependence of dielectric function and magnetic permeability on the frequency is considered. It is shown that for media with slow variation along one axis such a limit gives rise to the dispersionless Veselov-Novikov equation for the refractive index. It is demonstrated that the Veselov-Novikov hierarchy is amenable to the quasiclassical DBAR-dressing method. Under more specific requirements for the media, one gets the dispersionless Kadomtsev-Petviashvili equation. Geometrical optics interpretation of some solutions of the above equations is discussed.
引用
@article{arxiv.nlin/0403051,
title = {Integrable equations in nonlinear geometrical optics},
author = {Boris G. Konopelchenko and Antonio Moro},
journal= {arXiv preprint arXiv:nlin/0403051},
year = {2012}
}
备注
33 pages, 7 figures