On Integrability and Chaos in Discrete Systems
  The scalar nonlinear Schrodinger (NLS) equation and a suitable discretization are well known integrable systems which exhibit the phenomena of ``effective'' chaos. Vector generalizations of both the continuous and discrete system are discussed. Some attention is directed upon the issue of the integrability of a discrete version of the vector NLS equation. 
M. J. Ablowitz, Y. Ohta, A. D. Trubatch