Applications of moving frames to group foliation of differential equations

Loading...
Thumbnail Image

Persistent link to this item

Statistics
View Statistics

Journal Title

Journal ISSN

Volume Title

Title

Applications of moving frames to group foliation of differential equations

Published Date

2013-10

Publisher

Type

Thesis or Dissertation

Abstract

The classical group foliation algorithm uses the continuous symmetries of a differential equation to aid in its integration. This is accomplished by transforming the differential equation into two alternative systems, called the resolving and automorphic systems. Incorporating the theory of equivariant moving frames for Lie pseudogroups, a completely symbolic and systematic version of the group foliation algorithm is introduced. In this version of the algorithm, the resolving system is derived using only knowledge of the structure of the differential invariant algebra, requiring no explicit formulae for differential invariants. Additionally, the automorphic system is replaced by an equivalent reconstruction system, again requiring only symbolic computation. The efficacy of this approach is illustrated through several examples. Further applications of aspects of group foliation are given, including the construction of Backlund transformations using resolving systems and a reconstruction process for an invariant submanifold flow corresponding to a given invariant signature evolution.

Description

University of Minnesota Ph.D. dissertation. October 2013. Major: Mathematics. Advisor: Peter J. Oliver. 1 computer file (PDF); v, 112 pages.

Related to

Replaces

License

Collections

Series/Report Number

Funding information

Isbn identifier

Doi identifier

Previously Published Citation

Suggested citation

Thompson, Robert. (2013). Applications of moving frames to group foliation of differential equations. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/161144.

Content distributed via the University Digital Conservancy may be subject to additional license and use restrictions applied by the depositor. By using these files, users agree to the Terms of Use. Materials in the UDC may contain content that is disturbing and/or harmful. For more information, please see our statement on harmful content in digital repositories.