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Vector bundles and Lax equations on algebraic curves
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The Hamiltonian theory of zero-curvature equations with spectral parameter on an arbitrary compact Riemann surface is constructed. It is shown that the equations can be seen as commuting flows of an infinite-dimensional field generalization of the Hitchin system. The field analog of the elliptic Calogero-Moser system is proposed. An explicit parameterization of Hitchin system based on the Tyurin parameters for stable holomorphic vector bundles on algebraic curves is obtained.
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Cited by 2 Pith papers
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Gauge Theory And Integrability, III
A four-dimensional Chern-Simons gauge theory with surface defects systematically engineers two-dimensional integrable field theories with Lax operators.
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Elliptic Ruijsenaars-Toda and elliptic Toda chains: classical r-matrix structure and relation to XYZ chain
Elliptic Toda and Ruijsenaars-Toda chains are special cases of the elliptic Ruijsenaars chain with derived r-matrix structures and gauge equivalences to XYZ spin chains.
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