Multi-Hamiltonian Structure of Lotka-Volterra and Quantum Volterra   Models
  We consider evolution equations of the Lotka-Volterra type, and elucidate especially their formulation as canonical Hamiltonian systems. The general conditions under which these equations admit several conserved quantities (multi-Hamiltonians) are analysed. A special case, which is related to the Liouville model on a lattice, is considered in detail, both as aclassical and as aquantal system 
C. Cronstrom, M. Noga