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The purpose of this paper is twofold. The first is to apply the methodintroduced in the works of Nakayashiki and Smirnov on the Mumford system to itsvariants. The other is to establish a relation between the Mumford system andthe isospectral limit $\mathcal{Q}_g^{(I)}$ and $\mathcal{Q}_g^{(II)}$ of theNoumi-Yamada system. As a consequence, we prove the algebraically completelyintegrability of the systems $\mathcal{Q}_g^{(I)}$ and $\mathcal{Q}_g^{(II)}$,and get explicit descriptions of their solutions.Comment: 22 pages, an extensively revised versio

Cohomological Study on Variants of the Mumford System, and Integrability of the Noumi–Yamada System