Generalization of the double reduction theory

In a recent work Sjöberg (2007, 2008) [1] and [2] remarked that generalization of the double reduction theory to partial differential equations of higher dimensions is still an open problem. In this note we have attempted to provide this generalization to find invariant solution for a non linear system of qqth order partial differential equations with nn independent and mm dependent variables provided that the non linear system of partial differential equations admits a nontrivial conserved form which has at least one associated symmetry in every reduction. In order to give an application of the procedure we apply it to the nonlinear (2+1) wave equation for arbitrary function f(u)f(u) and g(u)g(u).