Symmetries of vector exterior differential systems and the inverse problem in second-order Ostrograds’kii mechanics. (English) Zbl 0957.58003

Matsyuk, R. Ya.

J. Nonlinear Math. Phys. 4, No. 1-2, 89-97 (1997).

The author recalls the vector bundle valued differential forms and exterior systems. Then he introduces a new kind of equivalence in order to reformulate the usual concepts of symmetries and infinitesimal symmetries of systems of differential equations: two exterior differential systems are called equivalent if the sets of their solutions coincide, the symmetry is a transformation which changes a given system into an equivalent system.
It is not easy to effectively apply this new conception, a simple example from the relativistic mechanics is nevertheless briefly mentioned.

Reviewer: Jan Chrastina (Brno)

MSC:

58A15	Exterior differential systems (Cartan theory)
58E30	Variational principles in infinite-dimensional spaces

Keywords:

infinitesimal summetry; Euler-Lagrange equation; exterior differential systems