Wave interaction for a generalized higher-dimensional Boussinesq equation describing the nonlinear Rossby waves

Based on an algebraically Rossby solitary waves evolution model, namely an extended (2+1)-dimensional Boussinesq equation, we firstly introduced a special transformation and utilized the Hirota method, which enable us to obtain multi-complexiton solutions and explore the interaction among the solutions. These wave functions are then employed to infer the influence of background flow on the propagation of Rossby waves, as well as the characteristics of propagation in multi-wave running processes. Additionally, we generated stereogram drawings and projection figures to visually represent these solutions. The dynamical behavior of these solutions is thoroughly examined through analytical and graphical analyses. Furthermore, we investigated the influence of the generalized beta effect and the Coriolis parameter on the evolution of Rossby waves.