On algebro-geometric Poisson brackets for the Volterra lattice
Mathematical Physics
2007-05-23 v2 Algebraic Geometry
math.MP
Exactly Solvable and Integrable Systems
Abstract
A generalization of the theory of algebro-geometric Poisson brackets on the space of finite-gap Schroedinger operators, developped by S. P. Novikov and A. P. Veselov, to the case of periodic zero-diagonal difference operators of second order is proposed. A necessary and sufficient condition for such a bracket to be compatible with higher Volterra flows is found.
Keywords
Cite
@article{arxiv.math-ph/0010027,
title = {On algebro-geometric Poisson brackets for the Volterra lattice},
author = {A. P. Veselov and A. V. Penskoi},
journal= {arXiv preprint arXiv:math-ph/0010027},
year = {2007}
}
Comments
8 pages, written addendum