Classical Poisson structures and r-matrices from constrained flows
solv-int
2009-10-28 v1 量子代数
可精确求解与可积系统
q-alg
摘要
We construct the classical Poisson structure and -matrix for some finite dimensional integrable Hamiltonian systems obtained by constraining the flows of soliton equations in a certain way. This approach allows one to produce new kinds of classical, dynamical Yang-Baxter structures. To illustrate the method we present the -matrices associated with the constrained flows of the Kaup-Newell, KdV, AKNS, WKI and TG hierarchies, all generated by a 2-dimensional eigenvalue problem. Some of the obtained -matrices depend only on the spectral parameters, but others depend also on the dynamical variables. For consistency they have to obey a classical Yang-Baxter-type equation, possibly with dynamical extra terms.
引用
@article{arxiv.solv-int/9509005,
title = {Classical Poisson structures and r-matrices from constrained flows},
author = {Yunbo Zeng and Jarmo Hietarinta},
journal= {arXiv preprint arXiv:solv-int/9509005},
year = {2009}
}
备注
16 pages in LaTeX