# A name for PDE systems which are neither under- nor overdetermined?

The concepts of overdetermined and underdetermined PDE systems are well known. However, all sources I have so far looked into appear to avoid giving any name to PDE systems which are neither overdetermined nor underdetermined. Is there any reasonably commonly used name for such PDE systems? If possible, please provide the references where the name from your answer is used.

EDIT: It was suggested by Igor Khavkine and Robert Bryant that one should consider formally integrable systems (which are neither over- nor underdetermined and have no nontrivial compatibility conditions). I like the idea but in my case this term would appear within the discussion of systems which are completely integrable (via the inverse scattering transform), and this might confuse the non-expert readers. Is there any sensible way out of this conundrum?

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Well-posed? Formally integrable? I guess it would depend if you are concerned with purely local or also with global properties. – Igor Khavkine Jun 22 '11 at 15:50
@Igor: I am interested in purely local properties. – mathphysicist Jun 22 '11 at 16:23
@Igor: Thanks for the suggestions, formally integrable sounds interesting. – mathphysicist Jun 22 '11 at 16:28
I would be a little wary of the definitions given for "overdetermined" and "underdetermined". Although they work for most examples that arise, they do not in general. – Deane Yang Jun 22 '11 at 17:47
I'm confused: why formally integrable? May overdetermined or underdetermined systems not also be formally integrabel? – Michael Bächtold Jun 22 '11 at 19:39