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Generating mechanism and dynamic of the smooth positons for the derivative nonlinear Schrödinger equation

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Abstract

Based on the degenerate Darboux transformation, the n-order smooth positon solutions for the derivative nonlinear Schrödinger equation are generated by means of the general determinant expression of the N-soliton solution, and interesting dynamic behaviors of the smooth positons are shown by the corresponding three-dimensional plots in this paper. Furthermore, the decomposition process, bent trajectory and the change of the phase shift for the positon solutions are discussed in detail. Additionally, three kinds of mixed solutions, namely (1) the hybrid of one-positon and two-positon solutions, (2) the hybrid of two-positon and two-positon solutions, and (3) the hybrid of one-soliton and three-positon solutions, are presented and their rather complicated dynamics are revealed.

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Funding

This work is supported by the Natural Science Foundation of Zhejiang Province under Grant Nos. LY15A010005 and LZ19A010001, the Natural Science Foundation of Ningbo under Grant No. 2018A610197, the NSF of China under Grant Nos. 11601187, 11671219, K. C. Wong Magna Fund in Ningbo University, Scientific Research Foundation of Graduate School of Ningbo University.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Ningbo University, Ningbo, 315211, Zhejiang, People’s Republic of China

    Wenjuan Song & Maohua Li

  2. College of Mathematics Physics and Information Engineering, Jiaxing University, Jiaxing, 314001, Zhejiang, People’s Republic of China

    Shuwei Xu

  3. Institute for Advanced Study, Shenzhen University, Shenzhen, 518060, Guangdong, People’s Republic of China

    Jingsong He

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  1. Wenjuan Song
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Song, W., Xu, S., Li, M. et al. Generating mechanism and dynamic of the smooth positons for the derivative nonlinear Schrödinger equation. Nonlinear Dyn 97, 2135–2145 (2019). https://doi.org/10.1007/s11071-019-05111-5

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