How to choose a Right Discretization of the Continuous System? A lot of important works were dedicated to this problem. Two different sources of the right discretizations of the systems with "soliton-type" hidden symmetry will be considered in the talk: the existence of the Euler-Darboux-Backlund and Laplace type transformations of the linear operators is the main source of our approach to the proper discretization of the linear and nonlinear systems.
