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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2017
• Main Authors: Güneysu, B., Pflaum, M.J.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2017
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148568
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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...