The application of group theory to the solution of partial differential equations was first considered by Lie [1] and later by Ovsjannikov [2] and Matschat and Miiller [3]. If a one-parameter group of transformations leaves invariant an equation and its accompanying boundary conditions, then the number of vari ables can be reduced by one. The functional form of the solution can be deduced by solving a first order partial differential equation derived from the infinitesimal version of the global group. The functional form of the solution for two inde pendent variables (x, t), say, is (1) u (x, t)= F (x, t, 7),/(rj)) where η is called the similarity variable. The dependence of F on x, t (for calculation purposes, as will be seen later, it is convenient to isola/(r?) is known explicitly from invariance considerations./(rj) satisfies nary differential equation obtained by substituting the form (1) into partial differential equation. The form (1) is called the general simila tion. Initially no special boundary conditions are imposed since event use the invariants of the group to establish the boundary conditions.