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The dynamics of some exact solutions of the (3+1)-dimensional generalized shallow water wave equation

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Abstract

The (3+1)-dimensional generalized shallow water wave equation is systematically investigated in this paper based on the Hirota bilinear method. The N-soliton solution and the higher-order kink-shaped breather solutions of the (3+1)-dimensional generalized shallow water wave equation are first proposed. Then, the line rogue wave solution and various hybrid solutions consisting of the breather, the kink-shaped soliton and the periodic solutions are discussed. Furthermore, the lump solutions of it are derived by using the long wave limit of the N-soliton solution. In addition, the diverse semi-rational solutions composed of lumps, kink solitons, line rogue wave and breathers enrich the research contents of the (3+1)-dimensional generalized shallow water wave equation. The dynamic behaviors of these exact solutions are vividly presented by their respective three-dimensional diagrams and density plots with contours.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 1211153003, the Natural Science Foundation of Ningbo under Grant No. 2018A610197, K. C. Wong Magna Fund in Ningbo University.

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The authors are supported by the NSF of Ningbo under Grant No. 2023J126.

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

    Lingna Ying & Maohua Li

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  1. Lingna Ying
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Ying, L., Li, M. The dynamics of some exact solutions of the (3+1)-dimensional generalized shallow water wave equation. Nonlinear Dyn 111, 15633–15651 (2023). https://doi.org/10.1007/s11071-023-08664-8

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