Variable coefficient extended cKP equation for Rossby waves and its exact solution with dissipation

Abstract

In this article, the variable coefficient (2 + 1)-dimensional extended cylindrical Kadomtsev–Petviashvili (cKP) equation describing Rossby waves was derived from the quasi-geostrophic potential vorticity equation. It is difficult for the variable coefficient cKP equation with dissipation to calculate the exact solution. For obtaining the exact solution, a new transformation was constructed for the first time to reduce the extended cKP equation to the extended KP equation. We emphasize that the exact solution, and not just approximate solution, in Rossby waves flow field can be obtained when dissipation is included. The exact lump and interaction solutions with dissipative effect are given according to the modified Hirota bilinear method, and physics for the evolution of Rossby waves is analyzed based on the obtained solutions. When the dissipative parameter μ0 increases, the structure of the amplitude A changes in the spatial scale y. And when the dissipative parameter increases to a certain value, the structure of Rossby waves tends to be stable. It is pointed out that the dissipative parameter μ0 determines not only the amplitude A of Rossby waves but also structures of Rossby waves flow field, with μ0 acting on the spatial scale y and the timescale t.