| Summary: | In the current study, the Rossby waves envelope near the equator is studied starting from a potential vorticity equation with the horizontal component of Coriolis parameter. Based on the equation, we first establish the amplitude evolution equation of the Rossby waves with complete Coriolis parameter and obtain rational function solutions by means of the subsidiary ordinary differential equation method with the help of chirp-free hypothesis. Then the 1-, 2-, 3-and N-soliton solutions are also obtained by the Hirota method. For these obtained solutions, they are rarely mentioned in fluid mechanics of ocean and atmospheric motion. On the other hand, these three-dimensional stereograms of the 1-, 2-soliton solutions are depicted with the physical parameter changing. The influence of each parameter on wave amplitude, the peak position and propagation direction of Rossby waves are discussed. The results show that the horizontal Coriolis parameter only alter the phase shift of the Rossby waves amplitude for the 1-soliton and 2-soliton solution. These results are of great significance for further theoretical research in geophysical fluid.
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