title: 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 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, the 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.
authors.affiliation: Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China.
authors.forename: Xiao-Yong
authors.initials: XY
authors.lastname: Wen
authors.affiliation: Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China.
authors.forename: Zhenya
authors.initials: Z
authors.lastname: Yan
authors.affiliation: Department of Physical Electronics, School of Electrical Engineering, Tel Aviv University, Tel Aviv 59978, Israel.
authors.forename: Boris A
authors.initials: BA
authors.lastname: Malomed