On formal theory of differential equations. II. (English) Zbl 0703.34001

Chrastina, Jan

Čas. Pěstování Mat. 114, No. 1, 60-105 (1989); corrections ibid. 114, No. 4, 411 (1989).

[For part I see ibid. 111, 353-383 (1986; Zbl 0638.35008).]
The main object of investigation is so-called diffieties which represent the infinite prolongations of general systems of PDE. The correspondence between ODE and diffieties is studied and the aim is to solve underdetermined systems of ODE (the number of unknown functions exceeds the number of equations). With the help of diffieties the original system of m-1 ODE for m unknown functions is replaced by its infinite prolongation and the Monge problem is reduced to the problem of the equivalence of Pfaffian systems.

Reviewer: Y.V.Rogovchenko

MSC:

34A05	Explicit solutions, first integrals of ordinary differential equations
58A15	Exterior differential systems (Cartan theory)
58A17	Pfaffian systems

Keywords:

diffieties; Monge problem; Pfaffian systems