A FAMILY OF DISCRETE INTEGRABLE COUPLING SYSTEMS AND ITS LIOUVILLE INTEGRABILITY

摘要

A discrete matrix spectral problem and corresponding family of discrete integrable sys- tems are discussed. A semi-direct sum of Lie algebras of four-by-four matrices is in- troduced, and the related integrable coupling systems of resulting discrete integrable systems are derived. The obtained discrete integrable coupling systems are all written in their Hamiltonian forms by the discrete variational identity. Finally, Liouville inte- grability of the family of obtained integrable coupling systems is demonstrated.