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

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dc.contributor.author Constantinescu, O.
dc.date.accessioned 2019-02-18T11:18:45Z
dc.date.available 2019-02-18T11:18:45Z
dc.date.issued 2012
dc.identifier.citation 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. uk_UA
dc.identifier.issn 1815-0659
dc.identifier.other 2010 Mathematics Subject Classification: 49N45; 58E30; 34A26; 37J30
dc.identifier.other DOI: http://dx.doi.org/10.3842/SIGMA.2012.059
dc.identifier.uri http://dspace.nbuv.gov.ua/handle/123456789/148385
dc.description.abstract 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-forms and study its formal integrability. We prove that P is involutive and there is only one obstruction for the formal integrability of this operator. The obstruction is expressed in terms of the curvature tensor R of the induced nonlinear connection. We recover some of the classes of Lagrangian semisprays: flat semisprays, isotropic semisprays and arbitrary semisprays on 2-dimensional manifolds. uk_UA
dc.description.sponsorship The author express his thanks to Ioan Bucataru for the many interesting discussions about the pape uk_UA
dc.language.iso en uk_UA
dc.publisher Інститут математики НАН України uk_UA
dc.relation.ispartof Symmetry, Integrability and Geometry: Methods and Applications
dc.title Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations uk_UA
dc.type Article uk_UA
dc.status published earlier uk_UA


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