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Symmetry 2018, 10(4), 100; doi:10.3390/sym10040100

Nonclassical Symmetries of a Power Law Harry Dym Equation

Department of Mathematics, University of Central Arkansas, Conway, AR 72035, USA
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Received: 31 January 2018 / Revised: 3 April 2018 / Accepted: 4 April 2018 / Published: 6 April 2018
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Abstract

It is generally known that classical point and potential Lie symmetries of differential equations can be different. In a recent paper, we were able to show for a class of nonlinear diffusion equation that the nonclassical potential symmetries possess all nonclassical symmetries of the original equation. We question whether this is true for the power law Harry Dym equation. In this paper, we show that the nonclassical symmetries of the power law Harry Dym equation and an equivalent system still possess special separate symmetries. However, we will show that we can extend the nonclassical method so that all nonclassical symmetries of the original power law Harry Dym equation can be obtained through the equivalent system. View Full-Text
Keywords: classical symmetry; nonclassical symmetry; Harry Dym equation classical symmetry; nonclassical symmetry; Harry Dym equation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Arrigo, D.J.; Weaver, A.N. Nonclassical Symmetries of a Power Law Harry Dym Equation. Symmetry 2018, 10, 100.

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