A generating scheme for conservation laws of discrete zero curvature equations and its application

Abstract

A generating scheme for conservation laws of discrete integrable equations, arising as discrete zero curvature equations, is presented from pairs of associated matrix spectral problems. An illustrative application to the Volterra lattice equation is made through a pair of 2 × 2 matrix spectral problems. The general theory is not limited to 2×2 matrix spectral problems but for arbitrary-order matrix spectral problems.