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Novel bright-dark mixed \(\textit{N}\)-soliton for the (\(3+1\))-component Mel’nikov system and its multi-component generalization

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Abstract

Based on the KP-hierarchy reductionmethod, we construct the novel bright-dark mixed N-soliton for the (\(3+1\))-component Mel’nikov system including 3-component short waves (SWs) and one-component long wave (LW) for all possible combinations of nonlinearity coefficients. It is verified that dark or bright solitons can exist in the SW components, but only bright solitons appear in the LW component. According to different combinations of solitons in three different SW components, the bright-dark mixed N-soliton for the (\(3+1\))-component Mel’nikov system is mainly discussed into two types that two-bright-one-dark and one-bright-two-dark solitons. Finally, the (\(3+1\))-component Mel’nikov system can be directly extended to (\(M+1\))-component (\(M\ge 3\)) case comprised of M-component SWs and one-component LW, and the bright-dark mixed N-soliton for the multi-component generalization is also given in Gram determinant form.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (Grant No. 12201578, 11871232) and Natural Science Foundation of Henan Province (Grant No. 222300420377, 212300410417), the Doctor Scientific Research Fund of Zhengzhou University of Light Industry and the Youth Core Teachers Foundation of Zhengzhou University of Light Industry.

Funding

This funding was supported by National Natural Science Foundation of China (GrantNumber 11871232), Natural Science Foundation of Henan Province (GrantNumbers 222300420377, 212300410417 and 12201578).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, 450002, Henan, China

    Tao Xu, Guoliang He & Ming Wang

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  1. Tao Xu
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  2. Guoliang He
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  3. Ming Wang
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Correspondence to Tao Xu.

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Xu, T., He, G. & Wang, M. Novel bright-dark mixed \(\textit{N}\)-soliton for the (\(3+1\))-component Mel’nikov system and its multi-component generalization. Nonlinear Dyn 111, 4657–4671 (2023). https://doi.org/10.1007/s11071-022-08049-3

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