Stability of discrete dark solitons in nonlinear Schrodinger lattices
  We obtain new results on the stability of discrete dark solitons bifurcating from the anti-continuum limit of the discrete nonlinear Schrodinger equation, following the analysis of our previous paper [Physica D 212, 1-19 (2005)]. We derive a criterion for stability or instability of dark solitons from the limiting configuration of the discrete dark soliton and confirm this criterion numerically. We also develop detailed calculations of the relevant eigenvalues for a number of prototypical configurations and obtain very good agreement of asymptotic predictions with the numerical data. 
D.E. Pelinovsky and P.G. Kevrekidis