Cohomological study on variants of the Mumford system, and integrability of the Noumi-Yamada system

TL;DR

This paper extends cohomological methods to variants of the Mumford system, establishing their algebraic integrability and explicit solutions, and relates them to the Noumi-Yamada system's isospectral limits.

Contribution

It applies cohomological techniques to new variants of the Mumford system and proves their integrability, linking them to the Noumi-Yamada system's limits.

Findings

Proves algebraic complete integrability of Noumi-Yamada system limits.

Provides explicit solutions for the systems.

Establishes a relation between Mumford variants and Noumi-Yamada limits.

Abstract

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.