We consider a system of coupled cubic nonlinear Schrödinger (NLS) equations i ∂ψj ∂t = − ∂ψj ∂x2 + ψj n ∑ k=1 αjk|ψk| j = 1, 2, . . . , n, where the interaction coefficients αjk are real. The spectral stability of solitary wave solutions (both bright and dark) is examined both analytically and numerically. Our results build on preceding work by Nguyen et al. and others. Specifically, we present...