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Nonclassical Symmetries of a Nonlinear Diffusion–Convection/Wave Equation and Equivalents Systems

Department of Mathematics, University of Central Arkansas, Conway, AR 72035, USA
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Academic Editor: Roman M. Cherniha
Symmetry 2016, 8(12), 140; https://doi.org/10.3390/sym8120140
Received: 7 August 2016 / Revised: 22 November 2016 / Accepted: 22 November 2016 / Published: 26 November 2016
It is generally known that classical point and potential Lie symmetries of differential equations (the latter calculated as point symmetries of an equivalent system) can be different. We question whether this is true when the symmetries are extended to nonclassical symmetries. In this paper, we consider two classes of nonlinear partial differential equations; the first one is a diffusion–convection equation, the second one a wave, where we will show that the majority of the nonclassical point symmetries are included in the nonclassical potential symmetries. We highlight a special case were the opposite is true. View Full-Text
Keywords: nonclassical symmetry; nonclassical potential symmetry; diffusion equation; wave equation nonclassical symmetry; nonclassical potential symmetry; diffusion equation; wave equation
MDPI and ACS Style

Arrigo, D.J.; Ashley, B.P.; Bloomberg, S.J.; Deatherage, T.W. Nonclassical Symmetries of a Nonlinear Diffusion–Convection/Wave Equation and Equivalents Systems. Symmetry 2016, 8, 140.

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