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Dark soliton solutions of the defocusing Hirota equation by the binary Darboux transformation

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Abstract

In this paper, we study the defocusing Hirota equation that describes the propagation of ultrashort pulses in optical fibers with third-order dispersion and self-steepening higher-order effects. By the limit technique, we construct the Nth-iterated binary Darboux transformation in the determinant form and present a complete proof. We derive the multi-dark soliton solutions from the nonzero background and discuss the properties of dark solitons through the figures for several sample solutions. Our results will be valuable to the study of the future development of dark solitons in long-distance optical communication system.

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Acknowledgements

This work was supported by the Shanghai Leading Academic Discipline Project under Grant No. XTKX2012, by the Technology Research and Development Program of University of Shanghai for Science and Technology, by Hujiang Foundation of China under Grant No. B14005 and by the National Natural Science Foundation of China under Grant No. 11201302. H. Q. Zhang also thanks the support by Young Scholars’ Visiting Program sponsored by Shanghai Municipal Education Commission.

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  1. College of Science, University of Shanghai for Science and Technology, P. O. Box 253, Shanghai, 200093, China

    Hai-Qiang Zhang & Sha-Sha Yuan

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  1. Hai-Qiang Zhang
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  2. Sha-Sha Yuan
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Correspondence to Hai-Qiang Zhang.

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Zhang, HQ., Yuan, SS. Dark soliton solutions of the defocusing Hirota equation by the binary Darboux transformation. Nonlinear Dyn 89, 531–538 (2017). https://doi.org/10.1007/s11071-017-3469-2

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