标题： 基本分数非线性波模型和孤立子 显示英文标题

标题： Basic fractional nonlinear-wave models and solitons

摘要： 这篇综述文章对分数介质中线性和非线性波传播的一维和二维模型进行了简明总结。 基本模型源自分数量子力学以及更符合实验需求的光学中模拟分数衍射的设置，这些模型基于Riesz定义的分数导数，其特征是相应的Lévy指数。 还概述了由包含立方或二次非线性项的分数模型产生的的一维孤子的基本种类。 特别是，证明了变分近似在许多情况下是相关的。 还介绍了最近在光纤激光器中实现分数群速度色散的实验成果的总结。 显示英文摘要

摘要： This review article provides a concise summary of one- and two-dimensional models for the propagation of linear and nonlinear waves in fractional media. The basic models, which originate from fractional quantum mechanics and more experimentally relevant setups emulating fractional diffraction in optics, are based on the Riesz definition of fractional derivatives, which are characterized by the respective Levy indices. Basic species of one-dimensional solitons, produced by the fractional models which include cubic or quadratic nonlinear terms, are outlined too. In particular, it is demonstrated that the variational approximation is relevant in many cases. A summary of the recently demonstrated experimental realization of the fractional group-velocity dispersion in fiber lasers is also presented.