Are there any software-based solutions, for MAPLE, MATLAB, MATHEMATICA or others to convert a PDE to canonical form ?
You can easily make transformations of variables in programs like Maple or Mathematica. I think that Matlab is not as suitable for this purpose as Maple or Mathematica. You can make transformations to a canonical form either differentiating by 'hands' in these programs or using special procedures. For example, in Maple you can use dchange command from PDEtools package. If you were more specific about a PDE in questions, I would probably give a more detailed answer.
Thanks Dmitry, the PDE at hand is given here https://www.physicsforums.com/threads/separation-of-variables-in-matlab.924764/#post-5837092
If you look at the third message by SeM from top.
I have access to MATHEMATICA online, could you point to a procedure with commands for it by chance?
You are welcome. Your PDE is a nonlinear one, so there is no general approach to simplify it. Probably you can try to simplify it with the help of point transformations, but I do not know for sure whether there is a function in Mathematica which is similar to dchange in Maple. You can look at this discussion https://mathematica.stackexchange.com/questions/80241/analogue-for-maples-dchange-change-of-variables-in-differential-expressions . You can also try to find some symmetries admitted by the equation in question and then find the corresponding reductions and their solutions, see, e.g. http://reference.wolfram.com/language/tutorial/DSolveLieSymmetryMethods.html .
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