Dimensional deformations of integrable systems: I. An approach to integrability in multidimensions
Dimensional deformations of integrable systems: I. An approach to integrability in multidimensions
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可积系统的维度变形：I. 多维可积性方法
DOI：
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发表时间：
1989
期刊：
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通讯作者：
P. Santini
中科院分区：
文献类型：
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作者：
P. Santini
作者提出了一种方法，即可积系统的维度变形，以自然、直接和统一的方式生成可积系统的高维类似物。在这种基于 Fokas 和作者 (1988) 开发的描述可积性代数方面的理论的方法中，作者探索了给定可积系统的代数结构，目标是生成更高维度的可积概括。这种方法在几个例子中进行了说明，并且导出了已知的以及新颖的可积系统。该方法的简单性还允许人们找出导致多维中几乎完全不存在可积结构的理论和技术问题。
The author proposes an approach, the dimensional deformations of integrable systems, to generate in a natural straightforward and unified manner high-dimensional analogues of integrable systems. In this approach based on the theory developed by Fokas and the author (1988) describing the algebraic aspects of integrability, the author explores the algebraic structure of given integrable systems, with the goal of generating integrable generalisations in higher dimensions. This approach is illustrated in several examples, and known as well as novel integrable systems are derived. The simplicity of the method also allows one to single out the theoretical and technical problems responsible for the almost total absence of integrable structures in multidimensions.