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arXiv · 1802.10556

The hierarchy of Poisson brackets for the open Toda lattice and its' spectral curves

K. L. Vaninsky
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Abstract

We establish a new representation of the infinite hierarchy of Pois- son brackets (PB) for the open Toda lattice in terms of its spectral curve. For the classical Poisson bracket (PB) we give a representation in the form of a contour integral of some special Abelian differential (meromorphic one-form) on the spectral curve. All higher brackets of the infinite hierarchy are obtained by multiplication of the one-form by a power of the spectral parameter.

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K. L. Vaninsky. 2018-02-28. The hierarchy of Poisson brackets for the open Toda lattice and its' spectral curves. https://doi.org/10.1016/j.geomphys.2018.10.006

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