Finite symmetry transformation groups and some exact solutions of the Wu-Zhang equation

In this paper, the finite symmetry transformation groups of the Wu-Zhang equation are presented by the new symmetry group method and symbolic computation. The Lie symmetry groups obtained via traditional Lie approaches can be recovered in case of restricting some arbitrary constants. Some exact solutions of the Wu-Zhang equation which contain double solitary-like wave solutions and some complexiton solutions are derived by the multiple Riccati equations rational expansion method. At the same time, the corresponding new solutions can also be constructed through the finite symmetry transformation groups obtained.