| A(2+1)-dimensional nonlinear model for Rossby waves in stratified fluids and its solitary solution |
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| 作者姓名： | 陈利国 杨联贵 张瑞岗 刘全生 崔继峰 |
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| 作者单位： | 1;School of Statistics and Mathematics;College of Science |
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| 摘 要： | In this paper,we investigate a(2+1)-dimensional nonlinear equation model for Rossby waves in stratified fluids.We derive a forced Zakharov–Kuznetsov(ZK)–Burgers equation from the quasigeostrophic potential vorticity equation with dissipation and topography under the generalized beta effect,and by utilizing temporal and spatial multiple scale transform and the perturbation expansion method.Through the analysis of this model,it is found that the generalized beta effect and basic topography can induce nonlinear waves,and slowly varying topography is an external impact factor for Rossby waves.Additionally,the conservation laws for the mass and energy of solitary waves are analyzed.Eventually,the solitary wave solutions of the forced ZK–Burgers equation are obtained by the simplest equation method as well as the new modified ansatz method.Based on the solitary wave solutions obtained,we discuss the effects of dissipation and slowly varying topography on Rossby solitary waves.
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| 关 键 词： | ROSSBY SOLITARY waves dissipation topography forced ZK–Burgers EQUATION simplest EQUATION METHOD modified ANSATZ METHOD |
| 收稿时间： | 2019-11-27 |
A(2+1)-dimensional nonlinear model for Rossby waves in stratified fluids and its solitary solution |
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| Li-Guo Chen.A(2+1)-dimensional nonlinear model for Rossby waves in stratified fluids and its solitary solution[J].Communications in Theoretical Physics,2020,72(4):45004-36. |
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| Authors: | Li-Guo Chen |
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| Institution: | 1.School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China;2.School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, China;3.College of Science, Inner Mongolia University of Technology, Hohhot 010051, China |
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| Abstract: | In this paper, we investigate a (2+1)-dimensional nonlinear equation model for Rossby waves in stratified fluids. We derive a forced Zakharov–Kuznetsov(ZK)–Burgers equation from the quasi-geostrophic potential vorticity equation with dissipation and topography under the generalized beta effect, and by utilizing temporal and spatial multiple scale transform and the perturbation expansion method. Through the analysis of this model, it is found that the generalized beta effect and basic topography can induce nonlinear waves, and slowly varying topography is an external impact factor for Rossby waves. Additionally, the conservation laws for the mass and energy of solitary waves are analyzed. Eventually, the solitary wave solutions of the forced ZK–Burgers equation are obtained by the simplest equation method as well as the new modified ansatz method. Based on the solitary wave solutions obtained, we discuss the effects of dissipation and slowly varying topography on Rossby solitary waves. |
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| Keywords: | Rossby solitary waves dissipation topography forced ZK–Burgers equation simplest equation method modified ansatz method |
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