Multiple-order breathers for a generalized (3+1)-dimensional Kadomtsev–Petviashvili Benjamin–Bona–Mahony equation near the offshore structure

In this paper, a generalized (3+1)-dimensional Kadomtsev–Petviashvili Benjamin–Bona–Mahony equation which describes the fluid flow in the case of an offshore structure, is investigated. Here, making use of the bilinear form and symbolic computation, we construct four kinds of rogue wave solutions consisting of independent breathers. Among these solutions, the fourth order rogue wave solution is rarely considered in nonlinear system. Exact locations of the highest and lowest peaks as well as the extreme values of the wave heights are systematically analyzed. The obtained rogue waves observe certain “circularity structure”, the highest or lowest peaks both sit at the same circular. Moreover, we show that the rogue waves are stable during the propagation.