Moving localized modes in nonlinear lattices

An analytical approach based on the perturbed discrete Ablowitz-Ladik equation is applied to investigate intrinsic localized modes for two different models of one-dimensional anharmonic lattices, namely, for a chain with nonlinear interatomic interaction and a chain with nonlinear on-site potential. It is shown that the motion of the localized modes is strongly affected by an effective periodic (Peierls-Nabarro) potential, but for the former model moving localized modes may still exist in a wide region of the mode parameters, whereas for the latter one they will be always captured by the lattice discreteness if the amplitude of the mode exceeds a certain threshold value.