Mumford系统变体的上同调研究及Noumi-Yamada系统的可积性
Cohomological study on variants of the Mumford system, and integrability of the Noumi-Yamada system
摘要：
本文件有两个目的。第一个是应用的方法介绍了在工程中的Nakayashiki和Smirnov的芒福德系统，其变种。二是建立了Mumford系统与Noumi-Yamada系统的等谱限$\mathcal{Q}_g^{(I)}$和$\mathcal{Q}_g^{(II)}$之间的关系。因此，我们证明了系统$\mathcal{Q}_g^{(I)}$和$\mathcal{Q}_g^{(II)}$的代数完全可积性，并得到了它们的解的明确描述。
英文摘要：
The purpose of this paper is twofold. The first is to apply the method introduced in the works of Nakayashiki and Smirnov on the Mumford system to its variants. The other is to establish a relation between the Mumford system and the isospectral limit $\mathcal{Q}_g^{(I)}$ and $\mathcal{Q}_g^{(II)}$ of the Noumi-Yamada system. As a consequence, we prove the algebraically completely integrability of the systems $\mathcal{Q}_g^{(I)}$ and $\mathcal{Q}_g^{(II)}$, and get explicit descriptions of their solutions.
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。
