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

2005/01/31 by Rei Inoue, Takao Yamazaki · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic Geometry and Number Theory #Characterization (materials science) #Complex system #Isospectral #Limit (mathematics) #Nonlinear Waves and Solitons #Polynomial and algebraic computation #Relation (database) #math-ph #math.AG #math.MP #msc:14H40 #msc:14H70 #msc:37K20

paper · pdf · doi:10.1007/s00220-006-0028-y

published in Communications in Mathematical Physics 265(3), 699-719 (Springer Science+Business Media) · 22 pages, an extensively revised version

arxiv created 2006/01/17 · openalex publication_date 2006/05/04 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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 Q_g^(I) and Q_g^(II) of the Noumi-Yamada system. As a consequence, we prove the algebraically completely integrability of the systems Q_g^(I) and Q_g^(II), and get explicit descriptions of their solutions.

Citations

• Sheaves in Topology
• Symmetric products of an algebraic curve
• Dressing chains and the spectral theory of the Schrödinger operator
• Théorie de Hodge : II