Poisson integrators for Volterra lattice equations
  The Volterra lattice equations are completely integrable and possess bi-Hamiltonian structure. They are integrated using partitioned Lobatto IIIA-B methods which preserve the Poisson structure. Modified equations are derived for the symplectic Euler and second order Lobatto IIIA-B method. Numerical results confirm preservation of the corresponding Hamiltonians, Casimirs, quadratic and cubic integrals in the long-term with different orders of accuracy. 
T. Ergen\c{c}, B. Karas\"ozen