Isomonodromy equations on algebraic curves, canonical transformations and Whitham equations

2001/12/11 by I. M. Krichever, I. Krichever, Krichever, I. · 3 citations
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Numerical methods for differential equations #advanced mathematical theories #hep-th #math.AG

paper · pdf · doi:10.48550/arxiv.hep-th/0112096

arxiv created 2001/12/11 · openalex publication_date 2001/12/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Hamiltonian theory of isomonodromy equations for meromorphic connections with irregular singularities on algebraic curves is constructed. An explicit formula for the symplectic structure on the space of monodromy and Stokes matrices is obtained. The Whitham equations for the isomonodromy equations are derived. It is shown that they provide a flat connection on the space of the spectral curves of the Hitchin systems.

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