Potential symmetries for some ordinary differential equations

Some diffusion equations admitting potential symmetries and the scaling gro up as a Lie symmetry are considered and some general results are obtained. For all the equations that we have studied, a set of potential symmetries a dmitted by the diffusion equation is "inherited" by the ODE that emerges as the reduced equation under the scaling group. Using these potential symmet ries we find that the order of the ODE can be reduced even if this equation does not admit point symmetries. Moreover, in the case for which the ODE a dmits a group of point symmetries, we find that the potential symmetries al low us to perform further reductions than its point symmetries.