Could anyone please suggest related papers or article about the topic related to my one question below?

Reduce PDE to ODE by dilation symmetry

I also cite a paper in the link above.

We know that if there are number of $n$ states, we need to find $"n-1"$ symmetries to reduce the PDE to ODE. For each iteration (there are $n-1$ iterations), we need to do some tedious but not difficult calculation.

Is there any advanced method based on symmetries reduction (of course, it might based on some special condition of the structure of problems) such that maybe we can take fewer steps?

Thanks in advance.