Is it true to say that for each PDE of second order, there is one single canonical form? (or at least to the extant of multiplication by a constant/function of the original variables).
So far it it appears to be quite true, based on the basic examples I've tried, but I'm hardly confidant about it.
Is it true at all? Is it true under certain conditions? (maybe only true per variable change but not necessarily for different transformations?)
If this is true, I'd very much appreciate a source for such a statement/proof.
Thanks in advance.