Stability of discrete breathers in nonlinear Klein-Gordon type lattices with pure anharmonic couplings

We consider the discrete breathers in one-dimensional nonlinear Klein-Gordon type lattices with pure anharmonic couplings. A discrete breather in the limit of vanishing couplings, i.e., the anti-continuous limit, consists of a number of in-phase or anti-phase excited particles, separated by particles at rest. Existence of the discrete breathers is proved for weak couplings by continuation from the anti-continuous limit. We prove a theorem which determines the linear stability of the discrete breathers. The theorem shows that the stability or instability of a discrete breather depends on the phase difference and distance between the two sites in each pair of adjacent excited sites in the anti-continuous solution. It is shown that there are two types of the dependence determined by the sign of alpha epsilon, where alpha and epsilon are parameters such that positive (respectively, negative) alpha represents hard (respectively, soft) on-site nonlinearity and positive (respectively, negative) epsilon represents attractive (respectively, repulsive) couplings. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4746690]