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Multi-rogue wave solutions for a generalized integrable discrete nonlinear Schrödinger equation with higher-order excitations

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Abstract

In this paper, we construct the discrete higher-order rogue wave (RW) solutions for a generalized integrable discrete nonlinear Schrödinger (NLS) equation. First, based on the modified Lax pair, the discrete version of generalized Darboux transformation is constructed. Second, the dynamical behaviors of first-, second- and third-order RW solutions are investigated in corresponding to the unique spectral parameter, higher-order term coefficient, and free constants. The differences between the RW solution of the higher-order discrete NLS equation and that of the Ablowitz–Ladik (AL) equation are illustrated in figures. Moreover, we explore the numerical experiments, which demonstrates that strong-interaction RWs are stabler than the weak-interaction RWs. Finally, the modulation instability of continuous waves is studied.

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Acknowledgements

This work of has been supported by the National Natural Science Foundations of China (Grant Numbers 12001361 and 11701510).

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Authors and Affiliations

  1. College of Arts and Sciences, Shanghai Polytechnic University, Shanghai, 201209, People’s Republic of China

    Jun Yang

  2. Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, 310023, People’s Republic of China

    Yan-Li Zhang & Li-Yuan Ma

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Yang, J., Zhang, YL. & Ma, LY. Multi-rogue wave solutions for a generalized integrable discrete nonlinear Schrödinger equation with higher-order excitations. Nonlinear Dyn 105, 629–641 (2021). https://doi.org/10.1007/s11071-021-06578-x

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