Symmetries and symmetry reductions of the coupled Burgers equation

Symmetry analysis is an important method used in almost all fields of natural science. In this paper, by means of the symmetry analysis, a new model, namely the coupled Burgers equations, which can be used to describe two-layer fluids is studied in detail. The Lie point symmetries of the model are obtained. By using the symmetries, four types of symmetry reductions are found. Some special types of exact solutions such as the rational solutions, travelling soliton solutions and non-travelling soliton solutions are explicitly given by solving the reduction equations.