The (3 + 1)-dimensional Benjamin–Ono equation: Painlevé analysis, rogue waves, breather waves and soliton solutions

Abstract

In this paper, we analyzed the (3 + 1)-dimensional Benjamin–Ono (BO) equation. We first demonstrated that the governing model is not integrable in the Painlevé sense. The rogue wave and the breather wave solutions are then achieved with the use of bilinear form. Furthermore, using a combination of Lie symmetry analysis with the new Kudryshov method, and the Riccati equation technique, the abundant soliton and singular periodic solutions were derived. The criteria for existence of such solutions are also provided. Consequently, the derived solutions are presented graphically through 3D, 2D and contour plots, which describe useful physical phenomena due to existence of the free parameters. Corresponding to the one-reduction, power series solution of BO equation is also obtained.