On formal theory of differential equations. I. (English) Zbl 0638.35008

Chrastina, Jan

Čas. Pěstování Mat. 111, 353-383 (1986).

The author presents essential features of a theory of invariants of general systems of partial differential equations with respect to invertible transformations in the widest sense. Classes of equivalent systems (“diffieties”) are represented by special Pfaffian systems in an infinite-dimensional space. The precise definition of the diffiety includes four properties “Loc”, “Dim”, “Clos” and “Fin”. The property “Clos” corresponds to the compatibility conditions for the classical approach, the property “Fin” ensures that differential equations involving a finite number of unknown functions are studied. Using methods of commutative algebra and of homological algebra the author proves results on associated ideals and develops a general theory of characteristics.

Reviewer: W.Watzlawek

MSC:

35A30	Geometric theory, characteristics, transformations in context of PDEs
58J70	Invariance and symmetry properties for PDEs on manifolds
58A17	Pfaffian systems

Keywords:

theory of invariants; general systems of partial differential equations; invertible transformations; diffieties; Pfaffian systems; compatibility; commutative algebra; homological algebra; characteristics