Soliton, lump and hybrid solutions of a generalized (2+1)-dimensional Benjamin-Ono equation in fluids

The Benjamin-Ono equation can be used to describe the propagation and interaction of internal waves in stratified deep fluids. In this paper, we investigate a generalized (2+1)-dimensional Benjamin-Ono equation. We discuss the analytic solutions, including soliton, lump, and hybrid solutions, as well as the dynamic behaviors of those for this equation. Firstly, multi-soliton solutions of this equation are derived using the Hirota bilinear method. By adjusting various parameters, we obtain different morphologies of soliton interactions. The wave number k affects the soliton \('\) $_{}^{\prime }$ s height and width. The interaction between two solitons can result in either attraction or repulsion. The parameters w and \(\delta \) $\delta$ influence the propagation velocity and position of the solitons, respectively. Secondly, lump solutions of this equation are obtained through the long-wave limit method. By adjusting the parameters w and t, the interactions between lumps can lead to fission and fusion. Finally, we obtain hybrid solutions of this equation by applying the long-wave limit method to partial functions. It is shown that collisions between lumps and solitons are elastic. We discuss the influence of specific parameters on these solutions of this equation, and the dynamic analysis will be visualized through 3D graphs, which has not been explored in the existing literature. The results of this study have potential applications in understanding relevant dynamical behaviors of oceanography and atmospheric science.