The hierarchy of Poisson brackets for the open Toda lattice and its' spectral curves
arXiv:1802.10556 · doi:10.1016/j.geomphys.2018.10.006
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.
21 pages