Group classifications, optimal systems and exact solutions to the generalized Thomas equations

In this paper, the complete group classifications are performed on the types of Thomas equations (TEs), which arise in the study of chemical exchange progress, etc., all of the vector fields of the equations are presented. Then, the optimal system of the general Thomas equation is given, and all of the symmetry reductions and exact solutions generated from the optimal system are investigated. Furthermore, the exact analytic solutions to the Thomas equations are obtained by the generalized power series method.