The dynamical characteristics of interaction solutions for the KP equation describing Rossby waves

Abstract

The extreme weather caused by Rossby waves has been receiving increasing attention due to the presence of the Coriolis force. In this paper, we start with the material conservation equation, utilize the coordinate transformation and the perturbation expansion method to derive the high-dimensional Kadomtsev–Peviashvili equation. N-soliton solutions and K-lump solutions are obtained via the bilinear method and the long-wave limit method. Then, we construct the appropriate auxiliary function to study interaction solutions formed by the above two solutions. By choosing suitable parameters, we gain a clear understanding of the movement trajectories of N-soliton solutions, K-lump solutions, and interaction solutions formed of the above two solutions in different times. It is also evident that the shapes of the solutions do not change during the movement, but when they collide with each other, the amplitude of the solutions will increase significantly. And with the change of time \(T,\) the relative positions of N-soliton solutions and K-lump solutions will also change.