On Moving Discrete Modes in Nonlinear Lattices

In this paper we summarize the results of our investigation of the moving localized structures in lattice like systems. Dynamics of discrete localized modes in cubic, cubic-quintic, saturable photorefractive lattice and in the Bose-Einstein condensate modelled by the nonpolynomial Schrodinger equation are considered in the framework of the Peierls-Nabarro barrier. Two approaches are numerically tested: free-energy approach and mapping analysis. We show that only the last one is appropriate.