Nonclassical symmetries of a power law Harry Dym equation

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.