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On the reductions and classical solutions of the Schlesinger equations

TitleOn the reductions and classical solutions of the Schlesinger equations
Publication TypeJournal Article
Year of Publication2007
AuthorsDubrovin, B, Mazzocco, M
JournalDifferential equations and quantum groups, IRMA Lect. Math. Theor. Phys. 9 (2007) 157-187
Abstract

The Schlesinger equations S(n,m) describe monodromy preserving\\r\\ndeformations of order m Fuchsian systems with n+1 poles. They\\r\\ncan be considered as a family of commuting time-dependent Hamiltonian\\r\\nsystems on the direct product of n copies of m×m matrix algebras\\r\\nequipped with the standard linear Poisson bracket. In this paper we address\\r\\nthe problem of reduction of particular solutions of “more complicated”\\r\\nSchlesinger equations S(n,m) to “simpler” S(n′,m′) having n′ < n\\r\\nor m′ < m.

URLhttp://hdl.handle.net/1963/6472

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