MASTER SYMMETRIES FOR DIFFERENTIAL-DIFFERENCE EQUATIONS OF THE VOLTERRA TYPE

It is demonstrated that in the case of integrable differential-difference equations similar to the well-known Volterra equation (unlike the Korteweg-de Vries and nonlinear Schrodinger equations) there are many instances in which local master symmetries can be found. Those master symmetries are new interesting examples of local evolution chains explicitly depending on the time and discrete variable and integrable in a special sense. The examples are constructed by a direct and elementary approach which enables one to get new integrable equations, using Miura type transformations.