Existence, stability and dynamics of solitary waves in spinor dynamical lattices

In this work, motivated by the context of spinor (F =1) Bose-Einstein condensates that can be described by a quasi-one-dimensional model, we examine three-component dynamical lattices which feature the mean-field nonlinearity of the spinor system. Starting at the anti-continuum limit of uncoupled lattice sites, we develop a systematic perturbative approach of the types of modes that can emerge, depending on the relative phase of the excited sites. We examine one-, two- and three-excited site states, offer a systematic analysis of their linear stability and observe typical manifestations of the corresponding instabilities, when the lattice coherent structures are found to be linearly unstable. Despite the significantly different eigenvalue count, interestingly, we find that in the configurations examined the principal stability features remain similar to the single-component dynamical lattice in the immediate vicinity of the anti-continuum limit.