Master symmetries and r-matrices for the Toda lattice
The Toda lattice is the Hamiltonian mechanical system \(({\mathbb{R}}^{2n}\), \(\sum^{N}_{i=1}dp_ i\wedge dq^ i\), \(H=\sum^{N}_{i=1}p^ 2_ i+\sum^{N}_{i=1}e^{q^ i-q^ i+1})\) with \(q^ 0=q^{N+1}=0\). This system is completely integrable via the well known Flaschka's transformation with respect to a linear Poisson bracket \(w_ 1.\) In the paper under review the author constructs in a very ingeniuous manner a sequence of Poisson brackets \((W_ n)_{n\in {\mathbb{N}}}\) such that respect to each of them the Toda lattice remains a completely integrable mechanical system, and also points out some of their properties.
scientific article; zbMATH DE number 4176528