Chin. Phys. B, 2019, Vol. 28(1): 010201    DOI: 10.1088/1674-1056/28/1/010201
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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
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.

Keywords:  AB-BA equivalence principle      nonlocal Burgers equation      periodic waves
Received:  11 September 2018      Revised:  13 October 2018      Accepted manuscript online:
 PACS: 02.30.Jr (Partial differential equations) 02.30.Ik (Integrable systems) 05.45.Yv (Solitons) 47.35.Fg (Solitary waves)
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