The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs
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| Creator |
Güneysu, B.
Pflaum, M.J. |
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| Description |
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.
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| Date |
2019-02-18T15:58:27Z
2019-02-18T15:58:27Z 2017 |
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| Type |
Article
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| Identifier |
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.
1815-0659 2010 Mathematics Subject Classification: 58A05; 58A20; 35A30 DOI:10.3842/SIGMA.2017.003 http://dspace.nbuv.gov.ua/handle/123456789/148568 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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