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The rational and semi-rational solutions to the Hirota Maccari system

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Abstract

In this paper, based on the KP hierarchy reduction method, we get the concrete form of semi-rational solutions to the Hirota–Maccari (HM) system. The semi-rational solutions describe a variety of solution types, such as lumps, breathers and line solitons. In addition, we simplify the representation of the higher-order semi-rational solutions of the HM equation and focus on the lump classification as well as the dynamics of mixed solutions about lumps and line solitons. Simultaneously, the modulation instability of the HM equation is also analyzed. The kinetics of semi-rational solutions for the HM system are subsequently discussed.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 11371326 and 11975145).

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Rui Wang, Yi Zhang, Xiao-tong Chen & Ru-suo Ye

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  1. Rui Wang
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  2. Yi Zhang
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  3. Xiao-tong Chen
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  4. Ru-suo Ye
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Correspondence to Yi Zhang.

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Wang, R., Zhang, Y., Chen, Xt. et al. The rational and semi-rational solutions to the Hirota Maccari system. Nonlinear Dyn 100, 2767–2778 (2020). https://doi.org/10.1007/s11071-020-05624-4

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  • DOI: https://doi.org/10.1007/s11071-020-05624-4

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