The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs
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 i...
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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2017 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2017
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148568 |
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| Цитувати: | 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-148568 |
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dspace |
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irk-123456789-1485682019-02-19T01:24:29Z The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs Güneysu, B. Pflaum, M.J. 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. 2017 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Güneysu, B. Pflaum, M.J. |
| spellingShingle |
Güneysu, B. Pflaum, M.J. The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Güneysu, B. Pflaum, M.J. |
| author_sort |
Güneysu, B. |
| title |
The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs |
| title_short |
The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs |
| title_full |
The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs |
| title_fullStr |
The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs |
| title_full_unstemmed |
The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs |
| title_sort |
profinite dimensional manifold structure of formal solution spaces of formally integrable pdes |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148568 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:29:44Z |
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