Stability of intersite dark solitons in a parametrically driven discrete nonlinear Schrödinger equation

In this paper, a parametrically driven discrete nonlinear Schrödinger equation will be considered for defocusing case. Analytical and numerical calculations will be performed to determine the existence and stability of intersite dark discrete solitons admitted by discrete nonlinear Schrödinger equation. It will be shown that a parametric driving can stabilizes intersite discrete dark solitons. Stability windows of all the fundamental solitons will be presented and approximations to the onset of instability will be derived using perturbation theory, with accompanying numerical results.