Original Articles

AN EXTENSION OF THE DIRECT METHOD VIA AN APPLICATION

Published in: Quaestiones Mathematicae
Volume 24 , issue 1 , 2001 , pages: 111–122

DOI: 10.1080/16073606.2001.9639778

Author(s): Qu Changzheng Department of Mathematics, Peoples Republic of China , F.M. Mahomed Department of Computational and Applied Mathematics, and Centre for Differential Equations, Continuum Mechanics and applications, South Africa

Keywords: 35L05 , 35L70 , 58J90 , 58J70 , 35L05 , 35L70 , 58J90 , 58J70

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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.

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