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.
@article{arxiv.cond-mat/0409009,
title = {Modulational Instabilities and Domain Walls in Coupled Discrete Nonlinear Schr\"odinger Equations},
author = {Z. Rapti and A. Trombettoni and P. G. Kevrekidis and D. J. Frantzeskakis and Boris A. Malomed and A. R. Bishop},
journal= {arXiv preprint arXiv:cond-mat/0409009},
year = {2015}
}