On integrable reductions of nonlinear equations of two-dimensional Toda chain type

Abstract

We consider nonlinear integrable differential-difference equations with three independent variables, two of which are continuous and one is discrete. Such equations, called chains, admit finite-field reductions associated with truncations in the discrete variable. We present reductions in the form of systems of nonlinear hyperbolic partial differential equations possessing complete sets of characteristic integrals in both characteristic directions.