论文标题
非线性和离散性：晶格中的孤子
Nonlinearity and discreteness: Solitons in lattices
论文作者
论文摘要
给出了基本模型的概述，该模型结合了其线性部分（即模型为动态晶格）和非线性在晶格或站点之间的非线性作用。所考虑的系统包括TODA和FRENKEL-KONTOROVA晶格（包括其耗散版本），以及离散的非线性Schroedinger（DNLS）和Ablowitz-Ladik（Al）类型的方程，以及以Salerno模型形式的DNLS-AL组合。离散性和非线性的相互作用引起了各种状态，最重要的是自我捕获的离散孤子。在审查中收集了一维（1d和2d）离散孤子的基本结果，包括具有嵌入式涡度的2D孤子，以及有关离散孤子迁移率的一些结果。主要的实验发现也被概述。还以一种简短的形式考虑了半污染类型的模型，以及由其支持的孤子的基本结果。在整个文本中讨论了涵盖评论主题的观点。
An overview is given of basic models combining discreteness in their linear parts (i.e. the models are built as dynamical lattices) and nonlinearity acting at sites of the lattices or between the sites. The considered systems include the Toda and Frenkel-Kontorova lattices (including their dissipative versions), as well as equations of the discrete nonlinear Schroedinger (DNLS) and Ablowitz-Ladik (AL) types, and DNLS-AL combination in the form of the Salerno model. The interplay of discreteness and nonlinearity gives rise to a variety of states, most important ones being self-trapped discrete solitons. Basic results for one- and two-dimensional (1D and 2D) discrete solitons are collected in the review, including 2D solitons with embedded vorticity, and some results concerning mobility of discrete solitons. Main experimental findings are overviewed too. Models of the semi-discrete type, and basic results for solitons supported by them, are also considered, in a brief form. Perspectives for the development of topics covered the review are discussed throughout the text.
