Symmetry Integrability and Geometry-Methods and Applications | |
The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs | |
article | |
Batu Güneysu1  Markus J. Pflaum2  | |
[1] Institut für Mathematik;Department of Mathematics, University of Colorado | |
关键词: profinite dimensional manifolds; jet bundles; geometric PDEs; formal integrability; scalar fields; | |
DOI : 10.3842/SIGMA.2017.003 | |
来源: National Academy of Science of Ukraine | |
【 摘 要 】
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.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO202106300001060ZK.pdf | 639KB | download |