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Inverse Scattering Transform and Soliton Classification of Higher-Order Nonlinear Schrödinger-Maxwell-Bloch Equations

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Abstract

We investigate higher-order nonlinear Schrödinger-Maxwell-Bloch equations using the Riemann-Hilbert method. We perform a spectral analysis of the Lax pair and construct a Riemann-Hilbert problem according to the spectral analysis. As a result, we obtain three types of multisoliton solutions. Based on the analytic solution and with a choice of corresponding parameter values, we obtain solutions of the breather type and a bell-shaped solution and find an interesting phenomenon of the collision of two soliton solutions. We hope that these results can be useful in modeling the wave propagation of a nonlinear optical field in an erbium-doped fiber medium.

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Acknowledgments

The authors thank the editor and the referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. School of Mathematics and Institute of Mathematical Physics, China University of Mining and Technology, Xuzhou, China

    Zhi-Qiang Li, Shou-Fu Tian, Wei-Qi Peng & Jin-Jie Yang

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  1. Zhi-Qiang Li
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  2. Shou-Fu Tian
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  3. Wei-Qi Peng
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Correspondence to Shou-Fu Tian.

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The authors declare no conflicts of interest.

This research was supported by the Postgraduate Research and Practice of Educational Reform for Graduate students in CUMT (Grant No. 2019YJSJG046), the Natural Science Foundation of Jiangsu Province (Grant No. BK20181351), the Six Talent Peaks Project in Jiangsu Province (Grant No. JY-059), the Qinglan Project of Jiangsu Province of China, the National Natural Science Foundation of China (Grant No. 11975306), the Fundamental Research Fund for the Central Universities (Grant Nos. 2019ZDPY07 and 2019QNA35), and the General Financial Grant from the China Postdoctoral Science Foundation (Grant Nos. 2015M570498 and 2017T100413).

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 203, No. 3, pp. 323–341, June, 2020.

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Li, ZQ., Tian, SF., Peng, WQ. et al. Inverse Scattering Transform and Soliton Classification of Higher-Order Nonlinear Schrödinger-Maxwell-Bloch Equations. Theor Math Phys 203, 709–725 (2020). https://doi.org/10.1134/S004057792006001X

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