Discreteness-Induced Oscillatory Instabilities of Dark Solitons
  We reveal that even weak inherent discreteness of a nonlinear model can lead to instabilities of the localized modes it supports. We present the first example of an oscillatory instability of dark solitons, and analyse how it may occur for dark solitons of the discrete nonlinear Schrodinger and generalized Ablowitz-Ladik equations. 
Magnus Johansson (Department of Physics and Measurement Technology,   Linkoping University, Sweden) and Yuri S. Kivshar (Opt...