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

Abstract

Abstract 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.