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Jul 2, 2021 at 12:07 vote accept Mark
May 22, 2020 at 16:24 comment added Mark Thank you for the answer. I didn't expect this angle of explanation (geometry of PDE), but from it I clearly see the problems that could happen if transformations of this kind exist. And I like this explanation. I guess I expected (deep down) that there is some easy change of variables (which I have never encountered) that could work in the case of systems $(1)$ and $(2)$. And of course the common sense says no. Thanks again.
May 22, 2020 at 12:32 history answered Robert Bryant CC BY-SA 4.0