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
Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, 100191, Beijing, China
2 Shen Yuan Honors College, Beijing University of Aeronautics and Astronautics, 100191, Beijing, China
Accepted: 9 April 2022
Published online: 27 May 2022
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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022