1999/01/25 by M. A. Olshanetsky, M. Olshanetsky, Olshanetsky, M. · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Geometry and complex manifolds #Nonlinear Waves and Solitons #math-ph #math.MP #nlin.SI #solv-int
paper · pdf · doi:10.48550/arxiv.math-ph/9901019
19 pages, Latex, Contribution in the Proceedings "Integrability: the Seiberg-Witten and Whitham Equations", Edinburgh, September 1998
arxiv created 1999/01/25 · arxiv updated 2009/11/30
In this survey we present the interpretation of isomondromy preserving equations on Riemann surfaces with marked points as reduced Hamiltonian systems. The upstairs space is the space of smooth connections of GL(N) bundles with simple poles in the marked points. We discuss relations of these equations with the Whitham quantization of the Hitchin systems and with the classical limit of the Knizhnik-Zamolodchikov-Bernard equations. The main example is the one-parameter family of Painlevé VI equation and its multicomponent generalization.