I am learning the Lie symmetry group method for PDEs. In my reading, all of the applications of this method are to calculate the exact solutions of PDEs. Are there any good references which provide successful applications of Lie symmetry group method for the study of a PDE, other than the calculation of exact solutions? Thank you very much.

P.S., I am not quite sure whether this question is “about research-level mathematics”. I posted it in math.stackexchange two days ago, and there is no answer until now. But I really need some help.