2006/10/10 by Boris Dubrovin, B. Dubrovin, Dubrovin, B. +3 · 1 citation
Mathematics · Physics and Astronomy · #32G34 (Primary) #34M55 #53D30 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons #math.CA #math.DG #msc:32G34 #msc:34M55 #msc:53D30
paper · pdf · doi:10.48550/arxiv.math/0610327
32 pages. To the memory of our friend Andrei Bolibruch
arxiv created 2006/10/10 · openalex publication_date 2006/10/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Schlesinger equations S(n,m) describe monodromy preserving deformations of order m Fuchsian systems with n+1 poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of n copies of m× m matrix algebras equipped with the standard linear Poisson bracket. In this paper we address the problem of reduction of particular solutions of ``more complicated'' Schlesinger equations S(n,m) to ``simpler'' S(n',m') having n'< n or m' < m.