In this article, the (2+1)-dimensional variable coefficients coupled Burgers equation (vcCBE) is investigated for the first time with the help of Lie symmetry analysis method. This equation is an important nonlinear physical model. The optimal system of the (2+1)-dimensional vcCBE is analyzed by Olver’s method. Then, the (2+1)-dimensional vcCBE is reduced on the basis of the optimal system to multiple sets of (1+1)-dimensional equations. Various types of soliton solutions are obtained by solving the reduced equations. The
G
′
/
G
-expansion method, tanh-coth method, and Riccati equation method are used respectively. Finally, the obtained solutions are analyzed dynamically and their kinetic behavior is investigated.
In this article, the (2+1) - dimensional variable coefficients
Broer-Kaup-Kupershmit equation is studied for the first time by Lie
symmetry analysis. The derivation process of generating elements of
vcBKK equation is given systematically, and the optimal system of the
one-dimensional subalgebras is determined. Furthermore vcBKK equation is
reduced based on the optimal system, and then the reduced equations are
solved with the help of the (G’/G)-expansion method. The images of
various kinds of exact solutions are drawn. Finally, according to the
conservation theorem, the conservation laws of vcBKK equation is
constructed.
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