The Problem of Integrable Discretization: Hamiltonian Approach
The Problem of Integrable Discretization: Hamiltonian Approach
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DOI：
10.1007/978-3-0348-8016-9
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发表时间：
2003-08
期刊：
影响因子：
--
通讯作者：
Y. Suris
中科院分区：
文献类型：
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作者：
Y. Suris
离散可积系统理论的一种探索，着重讨论以下一般性问题：如何将给定的可积微分方程组中的一个或多个独立变量离散化，同时保持可积性。这个问题（在精神上与几何积分这样一个现代数值分析分支有关）在书中被视为可积系统理论的一个不可分割的部分，也通常被称为孤子理论。大多数结果只能从最近的期刊出版物中获得，其中许多是新的。因此，这本书是一种百科全书离散可积系统。它结合了研究专著和手册的特点。它提供了一个广泛的参考书目和详细的书目注释在每一章的末尾。大部分是独立的，它将被研究生和研究生以及研究人员在该地区的可积动力系统。
An exploration of the theory of discrete integrable systems, with an emphasis on the following general problem: how to discretize one or several of independent variables in a given integrable system of differential equations, maintaining the integrability property? This question (related in spirit to such a modern branch of numerical analysis as geometric integration) is treated in the book as an immanent part of the theory of integrable systems, also commonly termed as the theory of solitons. Most of the results are only available from recent journal publications, many of them are new. Thus, the book is a kind of encyclopedia on discrete integrable systems. It unifies the features of a research monograph and a handbook. It is supplied with an extensive bibliography and detailed bibliographic remarks at the end of each chapter. Largely self-contained, it will be accessible to graduate and post-graduate students as well as to researchers in the area of integrable dynamical systems.