The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems

A new approach to Hamiltonian structures of integrable systems is proposed by making use of a trace identity. For a variety of isospectral problems that can be unified to one model ψx=Uψ, it is shown that both the related hierarchy of evolution equations and the Hamiltonian structure can be obtained from the same solution of the equation Vx=[U,V].