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Modulation instability, conservation laws and soliton solutions for an inhomogeneous discrete nonlinear Schrödinger equation

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Abstract

In this paper, an inhomogeneous discrete nonlinear Schrödinger equation is analytically investigated. The modulation instability condition and conservation laws are derived. By virtue of the discrete Darboux transformation, two types of explicit solutions on the vanishing and non-vanishing backgrounds are generated. Those results might be useful in the study of solitons propagation in discrete optical fibers.

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Acknowledgements

We express our sincere thanks to each member of our discussion group for their suggestions. This work has been supported by the Special Funds of the National Natural Science Foundation of China under Grant No. 11347165 and 61405137, by the Shanxi Province Science Foundation for Youths under Grant Nos. 2015021008 and 2014011005-4.

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  1. School of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, China

    Hui-Qin Hao, Rui Guo & Jian-Wen Zhang

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  1. Hui-Qin Hao
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  2. Rui Guo
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  3. Jian-Wen Zhang
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Correspondence to Hui-Qin Hao.

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Hao, HQ., Guo, R. & Zhang, JW. Modulation instability, conservation laws and soliton solutions for an inhomogeneous discrete nonlinear Schrödinger equation. Nonlinear Dyn 88, 1615–1622 (2017). https://doi.org/10.1007/s11071-017-3333-4

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