Classical $\bold{r}$-Matrices and Compatible Poisson Structures for Lax Equations on Poisson Algebras
Mathematical Physics
2009-11-11 v1 math.MP
Symplectic Geometry
Abstract
Given a classical -matrix on a Poisson algebra, we show how to construct a natural family of compatible Poisson structures for the Hamiltonian formulation of Lax equations. Examples for which our formalism applies include the Benny hierachy, the dispersionless Toda lattice hierachy, the dispersionless KP and modified KP hierachies, the dispersionless Dym hierachy etc.
Cite
@article{arxiv.math-ph/0506029,
title = {Classical $\bold{r}$-Matrices and Compatible Poisson Structures for Lax Equations on Poisson Algebras},
author = {Luen-Chau Li},
journal= {arXiv preprint arXiv:math-ph/0506029},
year = {2009}
}
Comments
28 pages