Higher-order vector discrete rogue-wave states in the coupled Ablowitz-Ladik equations: exact solutions and stability

Abstract

An integrable system of two-component nonlinear Ablowitz-Ladik (AL) equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system. Then, new higher-order discrete two-component RW solutions of the system are found by means of a newly derived discrete version of a generalized Darboux transformation. Finally, perturbed evolution of these RW states is explored in terms of systematic simulations, which demonstrates that tightly and loosely bound RWs are, respectively, nearly stable and strongly unstable solutions.

arXiv comment21 pages, 15 figures, Chaos, 2016 in press

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• Two-dimensional fractional discrete NLS equations: dispersion relations, rogue waves, fundamental and vortex solitons