# Lie Groups and PDEs

A friend of mine recently explained to me a little bit about using Lie groups and symmetries to obtain solutions of PDEs. I was interested and wanted to learn a bit more about it. He's been using Olver's "Applications of Lie Groups to Differential Equations" but I found it a bit out of my reach.

I've taken a PDE course that followed Fritz John's "Partial Differential Equations" pretty closely, and a basic differential geometry course (curves and surfaces). I also have limited knowledge of group theory, but he said he didn't have any when he started learning the theory.

So my question is: should I study PDEs or group theory a bit more before attempting to tackle Olver's book, or should I try an easier text first?

Thanks for the help.

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Does Oliver's introduction say what the prerequisites are? Might be a good place to start. – BSteinhurst May 4 '11 at 0:07
Or just start reading Olver's book and take detours to learn what you need as you go along. – Deane Yang May 4 '11 at 1:17
Mathematical physics by Hassani has a chapter or two that is a kind of introduction to the material in Olver's book. I think this can be a good entry point (or it is possible that you decide Hassani's version is enough for now, but I doubt it because it is very interesting). – timur May 4 '11 at 2:43
According to Olver, his book is pretty self contained with regards to what it uses of Lie theory and manifolds. I think I'm going to follow Deane's suggestion and supplement it with an easier book, for examples, and such. – cako May 4 '11 at 4:09
Speaking as an outsider, I know that Olver's graduate text (now in a 1993 second edition) is highly regarded and is also virtually the only textbook covering this kind of material. It's clearly essential to start with specific examples as motivation for the use of general Lie group methods, which I think is the way Olver proceeds. This is very much in the spirit of Lie's original program, generalizing Galois theory from polynomial equations to differential equations. – Jim Humphreys May 4 '11 at 13:08