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

作者：Arrigo Daniel J^*; Ashley Brandon P; Bloomberg Seth J; Deatherage Thomas W

来源：Symmetry-Basel, 2016, 8(12): 140.

DOI：10.3390/sym8120140

• nonclassical symmetry
• nonclassical potential symmetry
• diffusion equation
• wave equation

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.

• 出版日期2016-12