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
(This article belongs to the Special Issue Lie and Conditional Symmetries and Their Applications for Solving Nonlinear Models)
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.
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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. https://doi.org/10.3390/sym8120140
AMA Style
Arrigo DJ, Ashley BP, Bloomberg SJ, Deatherage TW. Nonclassical Symmetries of a Nonlinear Diffusion–Convection/Wave Equation and Equivalents Systems. Symmetry. 2016; 8(12):140. https://doi.org/10.3390/sym8120140
Chicago/Turabian StyleArrigo, Daniel J.; Ashley, Brandon P.; Bloomberg, Seth J.; Deatherage, Thomas W. 2016. "Nonclassical Symmetries of a Nonlinear Diffusion–Convection/Wave Equation and Equivalents Systems" Symmetry 8, no. 12: 140. https://doi.org/10.3390/sym8120140
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