Discrete Systems and Integrability
Discrete Systems and Integrability
复制标题
DOI：
10.1017/cbo9781107337411
复制
发表时间：
2016-08
期刊：
影响因子：
--
通讯作者：
J. Hietarinta;N. Joshi;F. Nijhoff
中科院分区：
文献类型：
--
作者：
J. Hietarinta;N. Joshi;F. Nijhoff
这第一个介绍性文本离散可积系统介绍了关键概念的可积性从离散系统的Vantage地位，也使连续理论在相关的连接。在处理初级水平的材料的同时，这本书还强调了许多最近的发展。主题包括：达布和贝克伦德变换;差分方程和特殊函数;可积格方程的多维一致性;相关线性问题（Lax对）;与Pade逼近和收敛算法的联系;奇异性和几何; Hirota的格双线性形式;离散Painleve方程的有趣性质;以及拉格朗日多形的新理论。这本书以有机的方式构建材料，强调各种方法之间的相互联系，而论述主要是通过对关键示例的明确计算来完成的。由该领域受人尊敬的专家撰写，大量的练习和完整的参考文献列表将使高年级本科生和研究生以及其他学科的研究人员受益。
This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Backlund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Pade approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painleve equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thorough list of references will benefit upper-level undergraduate, and beginning graduate students as well as researchers from other disciplines.