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. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

This paper investigates a generalized (3+1)-dimensional Kadomtsev-Petviashvili Benjamin-Bona-Mahony equation describing fluid flow in offshore structures. Four kinds of rogue wave solutions, including a fourth order rogue wave solution, are constructed and systematically analyzed. The obtained rogue waves exhibit certain circularity structure and are shown to be stable during propagation.