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Discrete bright–dark soliton solutions and parameters controlling for the coupled Ablowitz–Ladik equation

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Abstract

We consider the nonautonomous discrete vector bright–dark solutions and their controllable behaviors in the coupled Ablowitz–Ladik equation with variable coefficients, which possesses complicated wave propagation in time. Based on the differential–difference symmetry transformation and the Lamé polynomial solutions, we use the Jacobi elliptic functions \(\hbox {sn}(n, m), \hbox {cn}(n, m)\), \(\hbox {dn}(n, m)\) and present the nonautonomous discrete vector bright–dark solutions, which are localized in space and keep the localization longer in time. Moreover, we also exhibit the wave propagation of nonautonomous Lamé polynomial solutions of higher order and their dynamics for some chosen parameters and functions. And the managements and dynamic behaviors of these solutions are investigated analytically.

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Acknowledgements

This work was supported by Natural Science Foundations of Liaoning Province, China (Grant No. 201602678) and (Grant No. 2015020029).

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  1. School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang, 110034, China

    Li Li & Fajun Yu

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  1. Li Li
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  2. Fajun Yu
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Correspondence to Fajun Yu.

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Li, L., Yu, F. Discrete bright–dark soliton solutions and parameters controlling for the coupled Ablowitz–Ladik equation. Nonlinear Dyn 89, 2403–2414 (2017). https://doi.org/10.1007/s11071-017-3593-z

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