Variable coefficient (2+1)D KP equation for Rossby waves and its dynamical analysis

We investigated the (2+1)D nonlinear Rossby waves with variable coefficients. When the group velocity is considered as a function of time in the stretch coordinates of employing multi-scale analysis, and the weak nonlinear perturbation expansions are used, the variable coefficient (2+1)D Kadomtsev-Petviashvili equation describing Rossby waves was derived from the quasi-geostrophic potential vorticity equation. For studying the effect of variable coefficients, Rossby soliton wave is obtained via auxiliary equation method. And from the results in Sect. 3.1, the variable coefficients cause not only the propagation of Rossby wave, but also the increase of its amplitude. For analyzing the rogue wave, we utilize the modified Hirota bilinear method, which has the advantage of structuring one test functions and calculating one time. Interestingly, the variable coefficients are limited to constants in Sect. 3.2. The physics for the evolutions of Rossby waves are analyzed. Through numerical simulations, the results show all blocking structures in this article move in longitude, and the blocking structures caused by soliton, lump and interaction wave, are depicted in the Rossby wave flow field.