Master symmetries for Volterra equation, Belov–Chaltikian and Blaszak–Marciniak lattice equations

It is shown how to derive master symmetries for nonlinear lattice equations systematically using the basic principles but without using either their zero curvature equations or the bi-Hamiltonian structure. This has been illustrated for Volterra equation, two coupled Belov–Chaltikian (BC), and three coupled Blaszak–Marciniak (BM) lattice equations. The existence of a sequence of master symmetries is one of the characteristics of completely integrable nonlinear partial differential and differential–difference equations admitting Hamiltonian structure.  2003 Elsevier Science (USA). All rights reserved