If one is given a differential equation, e. g. the KdV equation $\ u\_t + u\_{xxx} + uu\_x = 0$, how can he find all of the symmetries of the differential equation? Is there also a method that works for integral equations?



How to find the symmetry group of a differential equation
A very nice survey is given by Francesco Oliveri.


*Oliveri, Francesco*, [**Lie symmetries of differential equations: classical results and recent contributions**](http://dx.doi.org/10.3390/sym2020658), Symmetry 2, No. 2, 658-706 (2010). [ZBL1284.22014](https://zbmath.org/?q=an:1284.22014).


He has plenty of references, in particular to computer algebra system implementations of the algorithm (which goes back to Lie). See, e.g. reference 15.


See also [this mathematica stackexchange question](https://mathematica.stackexchange.com/questions/20438/symmetry-finding-packages) if you just care about the implementations.


