Article

 

The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs Öffentlichkeit 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
Zuletzt geändert
  • 2019-12-05
Resource Type
Urheberrechts-Erklärung
DOI
ISSN
  • 1815-0659
Language

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