@John Fredsted 1+: thank you for your post. But I need the symmetries of the strange PDE :).

@ecterrab Thank you for your efforts. But I am really looking for the symmetries of the strange PDE. I just came up with this PDE and i was facinated as I never saw something like this. That is why i called this PDE strange. The $u(0,t)$ is not a boundary value.

@Mac Dude I could not find it on Maplesoft's application website. I also contacted the author. I hope he will respond.

@Doug Meade Yeah MathJax is a must have for every mathematical forum :D.

@Kitonum Thank you alot that was exactly what I was looking for :).

@John Fredsted: I am working with a very long worksheet and sometimes I change something in the worksheet. As referencing all equations with new variable names is very tedious I am referencing the previous equations with the ditto operator %, but if I execute something in the worksheet lets say line 10 and go back to line 20 (which was aimed to target the previous spacial equation by %) I cannot run this properly.

@Markiyan Hirnyk Thank you for your answer. But this does not solve my question. The ditto operator only references the previous equation which was executed not the result of the previous line.

@Torre Yes thank you :). I did not type the right expressions. Thank you for taking your time!

@John Fredsted It seems that this method cannot be used for more complicated expressions. Is there a direct way to construct the commutator table?

gc();
restart;

with(DifferentialGeometry);
with(LieAlgebras);

DGsetup([t, x, u], M);
v := evalDG(D_t):
w := evalDG(D_t*t+D_u):

LieBracket(v, w);

The last line gives me v, while the result should be \partial_x .

Any suggestion? A way to directly construct the commutator table would also be appreciated.

@John Fredsted Thank you! This was exactly what i was looking for :). I would like to give you a thumbs up, but my reputation is to low. As soon a I have more reputation I will give you a thumb up!