Hitchin Systems - symplectic maps and two - dimensional version
نویسنده
چکیده
The aim of this paper is two fold. First, we define symplectic maps between Hitchin systems related to holomorphic bundles of different degrees. It allows to construct the Bäcklund transformations in the Hitchin systems defined over Riemann curves with marked points. We apply the general scheme to the elliptic Calogero-Moser (CM) system and construct the symplectic map to an integrable SL(N, C) Euler-Arnold top (the elliptic SL(N, C)-rotator). Next, we proposed a generalization of the Hitchin approach to 2d integrable theories related to holomorphic bundles of infinite rank. The main example is integrable two-dimensional version of the two-body elliptic CM system. The previous construction allows to define the symplectic map from the two-dimensional elliptic CM system to the Landau-Lifshitz equation.
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