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Lie group analysis, optimal system and analytic solutions of a (3+1)-dimensional generalized Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation for the fluid flow around an offshore structure

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Abstract

Offshore structures are used in the maritime engineering, oil industry, gas industry, energy-harvesting systems, transportation and aquaculture. In this paper, we investigate a (3+1)-dimensional generalized Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation for the fluid flow around an offshore structure. Lie point symmetry generators and Lie symmetry groups are constructed. Optimal system of the one-dimensional subalgebras is derived. According to that optimal system, we obtain certain symmetry reductions. Analytic solutions are obtained through those symmetry reductions, such as the hyperbolic-function, rational, trigonometric-function, power-series, periodic-wave and soliton solutions. This paper could be of some use for the future offshore-structure studies.

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Notes

  1. Relevant water-wave papers can be reviewed in Refs. [10, 11, 17,18,19,20].

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Acknowledgements

We express our sincere thanks to the Editors, Reviewers and all the members of our discussion group for their valuable comments. This work has been supported by the National Natural Science Foundation of China under Grant No. 11272023, and by the Fundamental Research Funds for the Central Universities.

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Authors and Affiliations

  1. Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China

    Liu-Qing Li, Yi-Tian Gao, Xin Yu & Fei-Yan Liu

  2. Shen Yuan Honors College, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China

    Liu-Qing Li

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  1. Liu-Qing Li
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  2. Yi-Tian Gao
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  3. Xin Yu
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Correspondence to Yi-Tian Gao or Xin Yu.

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Li, LQ., Gao, YT., Yu, X. et al. Lie group analysis, optimal system and analytic solutions of a (3+1)-dimensional generalized Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation for the fluid flow around an offshore structure. Eur. Phys. J. Plus 137, 629 (2022). https://doi.org/10.1140/epjp/s13360-022-02716-5

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