Multiple soliton solutions, lump, rogue wave and breather solutions of high dimensional equation for describing Rossby waves

•A high-dimensional Kadomtsev-Petviashvili equation is derived from a fluid system.•The soliton, lump, rogue wave and breather of this equation are achieved according to Hirota bilinear method.•The composite diagram of these solutions are depicted to observe the propagation properties of Rossby waves. In the past, we haven't paid much attention to higher-dimensional models, which are actually more consistent with the real atmosphere. In this manuscript, we derive a high-dimensional Kadomtsev-Petviashvili equation from a fluid system based on the Gardner-Morikawa transformation and the small parameter perturbation method, which is the first time to characterize the propagation process of Rossby waves in Large-scale atmospheric. The exact solutions such as soliton, lump, rogue wave and breather of this equation are achieved according to Hirota bilinear method and symbolic computation approach. Further we utilize the composite diagram of these solutions to observe the propagation properties of Rossby waves with assistance of Mathematica. The results enrich the analysis of Rossby waves in marine engineering and fluid dynamics.