Riccati型方程、广义WZNW方程和多维Toda系统
Riccati-type equations, generalised WZNW equations, and multidimensional Toda systems
摘要：
我们将李群的李代数的任意$\mathbb Z$ -阶化与一个Riccati型一阶微分方程组联系起来。考虑的特殊情况是普通的Riccati和矩阵Riccati方程。给出了这些方程的多维延拓。相关的Redheffer-里德微分系统的概括出现在一个自然的方式。建立了Toda系统与低维和高维Riccati型方程之间的联系。在这方面的可积性问题，这些方程进行了研究。作为例证，给出了与极大非交换Toda系统相关的可积多维Riccati型方程的一些例子。
英文摘要：
We associate to an arbitrary $\mathbb Z$-gradation of the Lie algebra of a Lie group a system of Riccati-type first order differential equations. The particular cases under consideration are the ordinary Riccati and the matrix Riccati equations. The multidimensional extension of these equations is given. The generalisation of the associated Redheffer--Reid differential systems appears in a natural way. The connection between the Toda systems and the Riccati-type equations in lower and higher dimensions is established. Within this context the integrability problem for those equations is studied. As an illustration, some examples of the integrable multidimensional Riccati-type equations related to the maximally nonabelian Toda systems are given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
