The interaction and dynamics of multi-Rossby soliton solutions in a variable coefficient inhomogeneous Zakharov–Kuznetsov equation with temporal bottom topography

This study derives and investigates the quasi-geostrophic vorticity equation with temporal bottom topography (where the bottom topography varies with time), together with its corresponding boundary conditions. During the derivation and analysis of the governing equation, the group velocity of the stretching transformation is treated as an indefinite integral function of time, leading to the formulation of the variable coefficient inhomogeneous Zakharov–Kuznetsov equation. Spatially varying coefficients is considered within the bottom topography contains spatially varying coefficients, constituting the governing factor that triggers the generation of variable coefficients. The ZK equation is simplified via a constructed transformation and the derivation of multi-Rossby soliton solutions is facilitated by Hirota bilinear method. Results analysis and numerical simulations reveal that Rossby waves exhibit irregular propagation characteristics, with their amplitudes dynamically evolving over time. As time progresses, multi-solitons undergo coupling and interaction in the flow field; furthermore, as the β parameter in the flow field increases, the impact of the dipole-structured blocking phenomenon gradually intensifies. These findings contribute new insights to the academic research in atmospheric dynamics.