Dark beam excitations in the defocusing (2+1)-dimensional Zakharov system

The defocusing (2+1)-dimensional Zakharov system describes beams that involve three independent variables: the propagation distance and two orthogonal coordinates. Consequently, it can be inferred from the system characteristics that such beams exhibit considerably richer nonlinear behavior than the (1+1)-dimensional systems. In this paper, using the Hirota bilinear method, we found analytical dark beam solutions of the defocusing (2+1)-dimensional Zakharov system, describing beams in normal regions of nonlinear media. Based on the parameters describing dark beam solutions, some characteristics are discussed, and the impact of these parameters on the propagation of such beams is analyzed. Our results indicate that the shape of dark beams can be completely controlled by adjusting these physical parameters. In addition to finding order-1 dark beams, we also obtain the analytical order-2 dark beam solutions and the order-n dark beam solutions of the system mentioned above, and discuss those in special cases. Interestingly, it turned out that such solutions can be simplified to breathers and rogue waves. An interesting special case is that of the dark Peregrine soliton, which can be considered as the basic dark rogue wave. The basic idea of nonlinear wave control that was used in this paper can be extended to other higher-dimensional nonlinear systems.