Evolution and interaction of soliton solutions of Rossby waves in geophysical fluid mechanics

Here, we study a nonlinear evolution equation with the dissipation effect, which is derived from potential vorticity equation of geophysical fluid mechanics with Coriolis parameter and dissipation term by using coordinate transformation method and perturbation expansion method. To better understand the propagation characteristics and interactions of Rossby waves soliton, the two-soliton and three-soliton solutions of the model equation are obtained by using the Hirota bilinear method. Then, we discuss the influence of the physical parameters on Rossby waves soliton amplitude and periodic based on the three-soliton solutions in detail, in addition, how to select parameters reasonably to control the amplitude, evolution, periodic of the soliton are given by researching the interactions of adjacent solitons. Also, we present the spatial transmission characteristics of Rossby waves. These consequences are of great significance to model Rossby solitary waves in atmospheric and oceanic dynamics.