Modulational Instabilities and Domain Walls in Coupled Discrete   Nonlinear Schr\"odinger Equations
  We consider a system of two discrete nonlinear Schr\"{o}dinger equations, coupled by nonlinear and linear terms. For various physically relevant cases, we derive a modulational instability criterion for plane-wave solutions. We also find and examine domain-wall solutions in the model with the linear coupling. 
Z. Rapti, A. Trombettoni, P.G. Kevrekidis, D.J. Frantzeskakis, Boris   A. Malomed and A.R. Bishop