The Lie symmetry analysis and dynamics of exact solutions for variable coefficients (2+1)-dimensional coupled burgers equation

Abstract

Abstract 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.