Key points are not available for this paper at this time.
The authors employ a general space and time transformation to find a class of second-order differential equations with the maximum number (eight) of Lie symmetry generators. They apply this transformation to obtain the symmetry generators for the harmonic oscillator and for a non-linear equation, introduced by Leach (1985), starting from the symmetry generators of the free-particle equation.
Duarte et al. (Sat,) studied this question.