A nonlocal Burgers equation in atmospheric dynamical system and its exact solutions*

Project supported by the National Natural Science Foundation of China (Grant Nos. 11405110, 11275129, and 11472177) and the Natural Science Foundationof Zhejiang Province of China (Grant No. LY18A050001).
Liu Xi-Zhong1, †, Yu Jun1, Lou Zhi-Mei1, Qian Xian-Min2
       

Two specific solutions of the nonlocal Burgers equation (24) with (25) expressed by (a) Eq. (32) and (b) Eq. (34) at a specific time τ = 1. The parameters are fixed as (a) a2 = b2 = e3 = e4 = e6 = c = 1, e5 = 2, a1 = 1/2, e2 = −2, ξ0 = τ0 = 0, m = 0.9; (b) a1 = a3 = b3 = e3 = e4=e5 = c = 1, e1 = 0, e2 = −4, e6 = 2, τ0 = 2, ξ0 = 0, m = 0.9.