Lie symmetry method for PDE/ODE

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I was wondering if anybody has any experience with Lie Symmetry Method for solving PDE and ODE's?

I have heard that the method is very general/systematic, but rather tedious and useless in practice. But recently I've noticed that Maple and Mathematica contain very nice functions, for example for finding symmetry groups for differential equations, and therefore minimizing the tedious work.

Im not expecting a magical method that finds exact solutions all the time. But a method that sometimes can help me exploiting symmetries in a PDE/ODE and/or the boundary conditions to simplify the problem, before doing an approximation (perturbation, HAM, etc). I'm thinking of both linear and non-linear (and coupled) equations.

Is this method worth studying for me, or do you think it will be a very disappointing experience?
 

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  • #2
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Well, seems like Lie symmetry method is not so well known in the physics community (or at least in here). If this is because the method is useless in practice or people are just not aware of its existence is hard to say. (The introduction of chapter 16 in this https://www.amazon.com/dp/0521884004/?tag=pfamazon01-20&tag=pfamazon01-20, suggests the second possibility).

When I find time, I shall study this method and report back my experience.

(But im still highly interested to hear about your experience, if any.)
 
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