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

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.