Article
The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs Public Deposited
https://scholar.colorado.edu/concern/articles/gt54kn800
- 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.
- Creator
- Date Issued
- 2017-01-09
- Academic Affiliation
- Journal Title
- Journal Volume
- 13
- Subject
- Last Modified
- 2019-12-05
- Resource Type
- Rights Statement
- DOI
- ISSN
- 1815-0659
- Language
Relationships
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Thumbnail | Title | Date Uploaded | Visibility | Actions |
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theProfiniteDimensionalManifoldStructureOfFormalSolutionS.pdf | 2019-12-05 | Public | Download | |
theProfiniteDimensionalManifoldStructureOfFormalSolutionS.pdf | 2019-12-05 | Public | Download |