Complete Integrability of General Nonlinear Differential-Difference Equations Solvable by the Inverse Method. II

Abstract

General nonlinear differential-difference equations solvable by the inverse method are shown to describe completely integrable hamiltonian systems. These equations emerge from a couple of linear eigenvalue equations with four potentials vn+1,1=zvn,1+Qnvn,2+Snvn+1,2, vn+1,2=z-1vn,2+Rnvn,1+Tnvn+1,1, which were proposed by Ablowitz and Ladik. An operator formulation based on the generalized Wronskian relation makes it possible to write down general nonlinear evolution equations of this class in the Hamiltonian forms.