Lie symmetry reductions and exact solutions of a coupled KdV-Burgers equation

In this paper, based on classical Lie group method, with the help of Maple software, we study a coupled KdV-Burgers equation, and get its infinitesimal generator, commutation table of Lie algebra, symmetry group and similarity reductions. In particular, solitary wave solutions and similarity solutions of the coupled KdV-Burgers equation are derived from the reduction equations.