Painlev\'{e} type equations and Hitchin systems
数学物理
2007-05-23 v1 math.MP
可精确求解与可积系统
solv-int
摘要
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 Painlev\'{e} VI equation and its multicomponent generalization.
引用
@article{arxiv.math-ph/9901019,
title = {Painlev\'{e} type equations and Hitchin systems},
author = {M. Olshanetsky},
journal= {arXiv preprint arXiv:math-ph/9901019},
year = {2007}
}
备注
19 pages, Latex, Contribution in the Proceedings "Integrability: the Seiberg-Witten and Whitham Equations", Edinburgh, September 1998