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A nonlocal Burgers equation in atmospheric dynamical system and its exact solutions |
| Xi-Zhong Liu(刘希忠)1, Jun Yu(俞军)1, Zhi-Mei Lou(楼智美)1, Xian-Min Qian(钱贤民)2 |
1 Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000, China;
2 Yuanpei College, Shaoxing University, Shaoxing 312000, China |
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Abstract From a two-vortex interaction model in atmospheric and oceanic systems, a nonlocal counterpart with shifted parity and delayed time reversal is derived by a simple AB reduction. To obtain some approximate analytic solutions of this nonlocal system, the multi-scale expansion method is applied to get an AB-Burgers system. Various exact solutions of the AB-Burgers equation, including elliptic periodic waves, kink waves and solitary waves, are obtained and shown graphically. To show the applications of these solutions in describing correlated events, a simple approximate solution for the two-vortex interaction model is given to show two correlated dipole blocking events at two different places. Furthermore, symmetry reduction solutions of the nonlocal AB-Burgers equation are also given by using the standard Lie symmetry method.
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Received: 11 September 2018
Revised: 13 October 2018
Published: 05 January 2019
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PACS:
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02.30.Jr
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(Partial differential equations)
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02.30.Ik
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(Integrable systems)
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05.45.Yv
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(Solitons)
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47.35.Fg
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(Solitary waves)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11405110, 11275129, and 11472177) and the Natural Science Foundation of Zhejiang Province of China (Grant No. LY18A050001). |
Corresponding Authors:
Xi-Zhong Liu
E-mail: liuxizhong123@163.com
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Cite this article:
Xi-Zhong Liu(刘希忠), Jun Yu(俞军), Zhi-Mei Lou(楼智美), Xian-Min Qian(钱贤民) A nonlocal Burgers equation in atmospheric dynamical system and its exact solutions 2019 Chin. Phys. B 28 010201
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