Propagation of lump-type waves in nonlinear shallow water wave

Hong-Yang Guan; Jian-Guo Liu; Hong-Yang Guan; Jian-Guo Liu

doi:10.3934/mbe.2023866

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 11: 19553-19564. doi: 10.3934/mbe.2023866

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Research article

Propagation of lump-type waves in nonlinear shallow water wave

Hong-Yang Guan ^{1
,
,},
Jian-Guo Liu ^{2
,
,}

1.
Department of Information Engineering, Liaoning University of Traditional Chinese Medicine, Shenyang 110847, China
2.
College of Computer, Jiangxi University of Chinese Medicine, Jiangxi 330004, China

Received: 25 August 2023 Revised: 29 September 2023 Accepted: 16 October 2023 Published: 25 October 2023

In this work, a new extended shallow water wave equation in (3+1) dimensions was studied, which represents abundant physical meaning in a nonlinear shallow water wave. We discussed the interaction between a lump wave and a single solitary wave, which is an inelastic collision. Further, the interaction between a lump wave and two solitary waves and the interaction between a lump wave and a periodic wave was also studied using the Hirota bilinear method. Finally, the interaction among lump, periodic and one solitary wave was investigated. The dynamic properties of the obtained results are shown and analyzed by some three-dimensional images.
- shallow water wave,
- lump wave,
- periodic wave,
- bilinear method
Citation: Hong-Yang Guan, Jian-Guo Liu. Propagation of lump-type waves in nonlinear shallow water wave[J]. Mathematical Biosciences and Engineering, 2023, 20(11): 19553-19564. doi: 10.3934/mbe.2023866

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Abstract

In this work, a new extended shallow water wave equation in (3+1) dimensions was studied, which represents abundant physical meaning in a nonlinear shallow water wave. We discussed the interaction between a lump wave and a single solitary wave, which is an inelastic collision. Further, the interaction between a lump wave and two solitary waves and the interaction between a lump wave and a periodic wave was also studied using the Hirota bilinear method. Finally, the interaction among lump, periodic and one solitary wave was investigated. The dynamic properties of the obtained results are shown and analyzed by some three-dimensional images.

References

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