Lie symmetry analysis, conservation laws and exact solutions for variable-coefficients (2+1)-dimensional dissipative long-wave system

The Lie symmetry analysis, optimal system, exact solutions and conservation laws of the (2+1) dimensional variable-coefficients dissipative long-wave (vcDLW) system are introduced in this paper. Lie symmetry analysis method is used to obtain the vector field firstly. And the Olver 's method is used to obtain the optimal system of one-dimensional subalgebras of the equations. Based on the optimal system, the equations are similarly reduced. Some representative equations are selected from the equations obtained after similarly reduction, and then the (G'/G)-expansion method is applied to these equations, so that some new exact solutions of the (2+1)-dimensional vcDLW equations can be obtained. Finally, we study the conservation laws of the system.