Two-dimensional discrete breathers: Construction, stability, and bifurcations

We develop a methodology for the construction of two-dimensional discrete b reather excitations. Application to the discrete nonlinear Schrodinger equa tion on a square lattice reveals three different types of breathers. Consid ering an elementary plaquette, the most unstable mode is centered on the pl aquette, the most stable mode is centered on its vertices, while the interm ediate (but also unstable) mode is centered at the middle of one of the edg es. Below the turning points of each branch in a frequency-power phase diag ram, the construction methodology fails and a continuation method is used t o obtain the unstable branches of the solutions until a triple point is rea ched. At this triple point, the branches meet and subsequently bifurcate in to the final, state of an extended phonon mode.