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Nonlinear dynamics of a generalized higher-order nonlinear Schrödinger equation with a periodic external perturbation

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Abstract

The nonlinear dynamics of a generalized higher-order nonlinear Schrödinger (HNLS) equation with a periodic external perturbation is investigated numerically. Via the phase plane analysis, we find that both the homoclinic orbits and heteroclinic orbits can exist for the unperturbed HNLS equation under certain conditions, which respectively corresponds to the bell-shaped and kink-shaped soliton solutions. Moreover, under the effect of the periodic external perturbation, the quasi-periodic bifurcations arise and can evolve into the chaos. The dynamical responses of the perturbed system varying with the perturbation strength and two types of chaotic attractors are discussed to show the existence of the chaotic motions. Via the feedback control methods, such chaotic motions are found to be controlled effectively and finally evolve into the stable quasi-periodic orbits. All the results are helpful to understand the dynamical properties of the nonlinear system.

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Acknowledgments

This work has been supported by the Fundamental Research Funds of the Central Universities (Project Nos. 2014QN30, 2014ZZD10 and 2015ZD16), by the National Natural Science Foundations of China (Grant Nos. 61505054, 11426105, 11305060 and 11371371), by the Postdoctoral Science Foundation of China (2014T70061) and by the Higher-Level Item Cultivation Project of Beijing Wuzi University (No. GJB20141001).

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Authors and Affiliations

  1. Department of Mathematics and Physics, North China Electric Power University, Beijing, 102206, China

    Min Li & Lei Wang

  2. School of Information, Beijing Wuzi University, Beijing, 101149, China

    Feng-Hua Qi

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  1. Min Li
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  2. Lei Wang
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  3. Feng-Hua Qi
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Correspondence to Min Li.

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Li, M., Wang, L. & Qi, FH. Nonlinear dynamics of a generalized higher-order nonlinear Schrödinger equation with a periodic external perturbation. Nonlinear Dyn 86, 535–541 (2016). https://doi.org/10.1007/s11071-016-2906-y

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  • DOI: https://doi.org/10.1007/s11071-016-2906-y

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