Stability of Discrete Solitons in the Presence of Parametric Driving

In this brief report, we consider parametrically driven bright solitons in the vicinity of the anti-continuum limit. We illustrate the mechanism through which these solitons become unstable due to the collision of the phase mode with the continuous spectrum, or eigenvelues bifurcating thereof. We show how this mechanism typically leads to complete destruction of the bright solitary wave.