Comparison of one-dimensional and two-dimensional discrete breathers

We present the similarities and differences between one-dimensional (1D) an d two-dimensional (2D) spatially localized, time periodic solutions in disc rete nonlinear Hamiltonian systems. In particular, the types of modes their stability and their bifurcations are presented. We find that two dimension s, apart from offering an additional mode compared with one dimension, exhi bit a much richer stability scenario. This is analyzed in detail using cont inuation techniques and linear stability analysis. (C) 2001 IMACS. Publishe d by Elsevier Science B.V. All rights reserved.