2000/11/05 by M. A. Olshanetsky, M. Olshanetsky, Olshanetsky, M.
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Black Holes and Theoretical Physics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #hep-th #nlin.SI
paper · pdf · doi:10.48550/arxiv.nlin/0011010
15 pages, Talk given at the CRM Workshop on Isomonodromic Deformations and Applications in Physics, Montreal, May, 2000
arxiv created 2000/11/05 · openalex publication_date 2000/11/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce new times in the monodromy preserving equations. While the usual times related to the moduli of complex structures of Riemann curves such as coordinates of marked points, we consider the moduli of generalized complex structures (W-structures) as the new times. We consider linear differential matrix equations depending on W-structures on an arbitrary Riemann curve. The monodromy preserving equations have a Hamiltonian form. They are derived via the symplectic reduction procedure from a free gauge theory as well as the associate linear problems. The quasi-classical limit of isomonodromy problem leads to integrable hierarchies of the Hitchin type. In this way the generalized complex structures parametrized the moduli of these hierarchies.