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

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

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 sys...

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Veröffentlicht in:Chaos (Woodbury, N.Y.) N.Y.), 2016-12, Vol.26 (12), p.123110-123110
Hauptverfasser: Wen, Xiao-Yong, Yan, Zhenya, Malomed, Boris A.
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Continuous radiation
Mathematical analysis
Nonlinear equations
Stability
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creator Wen, Xiao-Yong
Yan, Zhenya
Malomed, Boris A.
description 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.
doi_str_mv 10.1063/1.4972111
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subjects Continuous radiation
Mathematical analysis
Nonlinear equations
Stability
title Higher-order vector discrete rogue-wave states in the coupled Ablowitz-Ladik equations: Exact solutions and stability
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