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Generalized Darboux transformation, semi-rational solutions and novel degenerate soliton solutions for a coupled nonlinear Schrödinger equation

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Abstract

In this paper, we obtain two types of semi-rational solutions for a coupled nonlinear Schrödinger equation by applying generalized Darboux transformation (DT). Firstly, we obtain a new DT through a special limit process based on the traditional DT for the equation; then, some nonlinear wave interactions on the zero-intensity background are analyzed under the research of those semi-rational solutions. Based on the above discussion, the dynamics of the interactions between one regular soliton and the type-I degenerate solitons on the zero-intensity background are systematically analyzed by drawing the 3D- and 2D-dimensional plots.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11971475).

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Authors and Affiliations

  1. School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, Jiangsu, People’s Republic of China

    Hong-Yi Zhang & Yu-Feng Zhang

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  1. Hong-Yi Zhang
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  2. Yu-Feng Zhang
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Correspondence to Yu-Feng Zhang.

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Zhang, HY., Zhang, YF. Generalized Darboux transformation, semi-rational solutions and novel degenerate soliton solutions for a coupled nonlinear Schrödinger equation. Eur. Phys. J. Plus 136, 459 (2021). https://doi.org/10.1140/epjp/s13360-021-01400-4

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