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.
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
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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