Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2012
• ISSN: 1815-0659
• Main Author: Constantinescu, O.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2012
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148385
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations / O. Constantinescu // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 40 назв. — англ.

We address the integrability conditions of the inverse problem of the calculus of variations for time-dependent SODE using the Spencer version of the Cartan-Kähler theorem. We consider a linear partial differential operator P given by the two Helmholtz conditions expressed in terms of semi-basic 1-f...