The equations governing nonlinear light beam propagation in nematic liquid crystals form a [Formula: see text]-dimensional system consisting of a nonlinear Schrödinger-type equation for the electric field of the wavepacket and an elliptic equation for the reorientational response of the medium. The latter is “nonlocal” in the sense that it is much wider than the size of the beam. Due to these nonlocal, nonlinear features, there are no known general solutions of the nematic equations; hence, approximate methods have been found convenient to analyze nonlinear beam propagation in such media, particularly the approximation of solitary waves as mechanical particles moving in a potential. We review the use of dynamical equations to analyze solitary wave propagation in nematic liquid crystals through a number of examples involving their trajectory control, including comparisons with experimental results from the literature. Finally, we make a few general remarks on the existence and stability of optically self-localized solutions of the nematic equations.

中文翻译：

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非局域向列液晶中非线性光束的力学类比

控制向列液晶中非线性光束传播的方程形成了一个[公式：见正文]维系统，由波包电场的非线性薛定谔型方程和介质重新定向响应的椭圆方程组成。后者是“非局部的”，因为它比光束的大小要宽得多。由于这些非局部、非线性特征，没有已知的向列方程的一般解；因此，已经发现近似方法可以方便地分析这种介质中的非线性光束传播，特别是将孤立波近似为在势中移动的机械粒子。我们通过一些涉及其轨迹控制的示例，包括与文献中的实验结果进行比较，回顾了使用动力学方程来分析向列液晶中的孤立波传播。最后，我们对向列方程的光学自定位解的存在性和稳定性作了一些一般性的评论。