Symmetry properties and bi-Hamiltonian structure of the Toda lattice (Q1058216)

The authors study the exponential Toda-lattice, i.e. the system \(y_{ntt}=\exp [-(y_ n-y_{n-1})]-\exp [-(y_{n+1}-y_ n)],\) using the symmetry approach. A hereditary operator admitting a symplectic- implectic factorization is found. Consequently, the Hamiltonian and the bi-Hamiltonian structure is derived. One obtains the constants of motion and an infinite set of commuting Lie-Bäcklund symmetries.