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

摘要

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