Application of Lie groups and differentiable manifolds to general methods for simplifying systems of partial differential equations

General techniques are developed to obtain: (1) the completion of a sys- temof nonlinear first-order partid differential equations (PDES) which is an indepem dent set of further PDES derivable from the system by differentiation and elimination; and (2) simplifications of the system by choosing appropriate new independent and dependent variables using a result from Lie group theory The number of dependent and independent variables is reduced to the minimum. The theory specializes to the clasricd theory of a single nonlinear PDE with one unknown and can be combined with the methods of Olver, Edelen and Estabmok and Wahlquist. Most of the meth- ods appear to be sufficiently well defined for automation as are the techniques in Olvcr. A second-order nonlinear equation in n dimensions is given which is related to a fuoctional differential equation in statistical mechanics. It is reducible to two dimensions for any value of n 2 2.