Comparison of one-dimensional and two-dimensional discrete breathers

We present the similarities and differences between one-dimensional (1D) and two-dimensional (2D) spatially localized, time periodic solutions in discrete nonlinear Hamiltonian systems. In particular, the types of modes their stability and their bifurcations are presented. We find that two dimensions, apart from offering an additional mode compared with one dimension, exhibit a much richer stability scenario. This is analyzed in detail using continuation techniques and linear stability analysis.