标题： 分数介质中的光学孤子和涡旋：近期结果的简要综述 显示英文标题

标题： Optical solitons and vortices in fractional media: A mini-review of recent results

摘要： 文章对一些最近的结果进行了简要回顾，这些结果预测了在基于非线性薛定谔方程的模型中，孤子和孤立涡旋的稳定传播，这些模型包括分数维的一维或二维衍射以及立方或立方-五次非线性项，以及线性势。分数衍射由Riesz类型的分数阶空间导数表示，这些导数是通过直接和逆傅里叶变换定义的。以这种形式，可以通过光学装置中特殊设计的镜片、透镜和相位掩模组合的空间域光传播来实现。文章中呈现的结果主要是以数值形式获得的。也包含了一些分析结果——特别是对于快速移动的孤子以及变分近似产生的结果。还简要考虑了由分数复数Ginzburg-Landau方程描述的耗散孤子。 显示英文摘要

摘要： The article produces a brief review of some recent results which predict stable propagation of solitons and solitary vortices in models based on the nonlinear Schroedinger equation including fractional one- or two-dimensional diffraction and cubic or cubic-quintic nonlinear terms, as well as linear potentials. The fractional diffraction is represented by fractional-order spatial derivatives of the Riesz type, defined in terms of the direct and inverse Fourier transform. In this form, it can be realized by spatial-domain light propagation in optical setups with a specially devised combination of mirrors, lenses, and phase masks. The results presented in the article were chiefly obtained in a numerical form. Some analytical findings are included too -- in particular, for fast moving solitons, and results produced by the variational approximation. Also briefly considered are dissipative solitons which are governed by the fractional complex Ginzburg-Landau equation.