As time slowly progresses, so the mathematicians associated with the area of symmetry methods become more familiar. To keep things ticking over here, below is a brief list of some of the people associated with symmetry methods and their application to differential equations (in no particular order):
Peter Olver >> Peter Hydon >> Nail Ibragimov (who made the news in South Africa, no less, with symmetries) >> Peter Clarkson >> Liz Mansfield
There is also a research centre that deals with Lie group analysis and it's applications to mathematics. Although I am not altogether familiar with this research centre, it does seem to be quite interesting and worthy of further exploration.
Of course, there is one main person missing from the above list; an excellent biography of Sophus Lie can be found at the MacTutor History of Mathematics. The following quote, from Robert Hermann's book:
"In reading Lie's work in preparation for my commentary on these translations, I was overwhelmed by the richness and beauty of the geometric ideas flowing from Lie's work. Only a small part of this has been absorbed into mainstream mathematics. He thought and wrote in grandiose terms, in a style that has now gone out of fashion, and that would be censored by our scientific journals! The papers translated here and in the succeeding volumes of our translations present Lie in his wildest and greatest form."