Staggered and moving localized modes in dynamical lattices with the cubic-quintic nonlinearity

Results of a comprehensive dynamical analysis are reported for several fundamental species of bright solitons in the one-dimensional lattice modeled by the discrete nonlinear Schrodinger equation with the cubic-quintic nonlinearity. Staggered solitons, which were not previously considered in this model, are studied numerically, through the computation of the eigenvalue spectrum for modes of small perturbations, and analytically, by means of the variational approximation. The numerical results confirm the analytical predictions. The mobility of discrete solitons is studied by means of direct simulations, and semianalytically, in the framework of the Peierls-Nabarro barrier, which is introduced in terms of two different concepts, free energy and mapping analysis. It is found that persistently moving localized modes may only be of the unstaggered type.