The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs

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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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dc.contributor.author	Güneysu, B.
dc.contributor.author	Pflaum, M.J.
dc.date.accessioned	2019-02-18T15:58:27Z
dc.date.available	2019-02-18T15:58:27Z
dc.date.issued	2017
dc.identifier.citation	The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs / B. Güneysu, M.J. Pflaum // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 50 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 58A05; 58A20; 35A30
dc.identifier.other	DOI:10.3842/SIGMA.2017.003
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/148568
dc.description.abstract	In this paper, we study the formal solution space of a nonlinear PDE in a fiber bundle. To this end, we start with foundational material and introduce the notion of a pfd structure to build up a new concept of profinite dimensional manifolds. We show that the infinite jet space of the fiber bundle is a profinite dimensional manifold in a natural way. The formal solution space of the nonlinear PDE then is a subspace of this jet space, and inherits from it the structure of a profinite dimensional manifold, if the PDE is formally integrable. We apply our concept to scalar PDEs and prove a new criterion for formal integrability of such PDEs. In particular, this result entails that the Euler-Lagrange equation of a relativistic scalar field with a polynomial self-interaction is formally integrable.	uk_UA
dc.description.sponsorship	The first named author (B.G.) is indebted to W.M. Seiler for many discussions on jet bundles, and would also like to thank B. Kruglikov and A.D. Lewis for helpful discussions. B.G. has been financially supported by the SFB 647: Raum–Zeit–Materie, and would like to thank the University of Colorado at Boulder for its hospitality. The second named author (M.P.) has been partially supported by NSF grant DMS 1105670 and by a Simons Foundation collaboration grant, award nr. 359389. M.P. would also like to thank Humboldt-University, Berlin and the Max-Planck-Institute for Mathematics of the Sciences, Leipzig for their hospitality. Last but not least the authors thank the anonymous referees for constructive advice which helped to improve the paper.	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	The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA