Nonclassical Symmetries of a Nonlinear Diffusion–Convection/Wave Equation and Equivalents Systems
Department of Mathematics, University of Central Arkansas, Conway, AR 72035, USA
*
Author to whom correspondence should be addressed.
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.
View Full-Text
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
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.
Show more citation formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
