Solitonic interactions for Rossby waves with the influence of Coriolis parameters

• Published in: Results in physics 2021-09, Vol.28, p.104593, Article 104593
• Main Authors: Yin, XiaoJun, Liu, QuanSheng, Ma, ShengYun, Bai, ShuTing
• Format: Article
• Language: English
• Subjects: Rossby waves; Soliton; Subsidiary ordinary differential equation; The Hirota method
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2021.104593

•A nonlinear Schrödinger equation under a potential vorticity equation with the horizontal component of Coriolis parameter and the generalized beta approximation is derived by using the perturbation expansion method and multiple temporal and spatial scales method.•The rational function solutions are formally obtained by means of the subsidiary ordinary differential equation method with the help of chirp-free hypothesis.•The 1-, 2-, 3-and N-soliton solutions are also obtained by using the Hirota method.•The influence of each physical parameter on wave amplitude, the peak value and propagation direction of Rossby waves and control of physical parameters are discussed. 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.