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.

On the reductions and classical solutions of the Schlesinger equations / Dubrovin, Boris; Mazzocco, M.. - 9:(2007), pp. 157-187. [10.4171/020]

On the reductions and classical solutions of the Schlesinger equations

Dubrovin, Boris;
2007-01-01

Abstract

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.
2007
9
Differential equations and quantum groups, Andrey A. Bolibrukh memorial volume
157
187
http://preprints.sissa.it/xmlui/handle/1963/6472
Dubrovin, Boris; Mazzocco, M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/15099
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