Integrable two-dimensional lattices. Characteristic Lie rings and classification

This paper is devoted to the problem of classification of integrable nonlinear models with three independent variables. The classification algorithm based on the notion of characteristic Lie rings is applied to a class of the two-dimensional lattices of hydrodynamic type. By imposing appropriate cutting-off boundary conditions, we reduce the lattice to a system of the hyperbolic equations, which is assumed to be a Darboux integrable system. As a result, we found a new integrable lattice.