AN EXTENSION OF THE DIRECT METHOD VIA AN APPLICATION

Abstract

The Direct Method due to Clarkson and Kruskal [9] for finding similarity reductions of partial differential equations is extended to obtain similarity reductions of nonlinear partial differential equations with arbitrary functions. The extension is illustrated by the nonlinear hyperbolic equation with arbitrary wave velocity. The known results of symmetry reductions [2] for this equation are recovered by an extension of the direct method.