Journal of Nonlinear Mathematical Physics

Volume 11, Issue 2, May 2004, Pages 233 - 242

Self-Invariant Contact Symmetries

Authors
Peter E. Hydon
Corresponding Author
Peter E. Hydon
Received 22 September 2003, Accepted 8 January 2004, Available Online 1 May 2004.
DOI
10.2991/jnmp.2004.11.2.8How to use a DOI?
Abstract

Every smooth second-order scalar ordinary differential equation (ODE) that is solved for the highest derivative has an infinite-dimensional Lie group of contact symmetries. However, symmetries other than point symmetries are generally difficult to find and use. This paper deals with a class of one-parameter Lie groups of contact symmetries that can be found and used. These symmetry groups have a characteristic function that is invariant under the group action; for this reason, they are called `self-invariant.' Once such symmetries have been found, they may be used for reduction of order; a straightforward method to accomplish this is described. For some ODEs with a onparameter group of point symmetries, it is necessary to use self-invariant contact symmetries before the point symmetries (in order to take advantage of the solvability of the Lie algebra). The techniques presented here are suitable for use in computer algebra packages. They are also applicable to higher-order ODEs

Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
11 - 2
Pages
233 - 242
Publication Date
2004/05/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2004.11.2.8How to use a DOI?
Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Peter E. Hydon
PY  - 2004
DA  - 2004/05/01
TI  - Self-Invariant Contact Symmetries
JO  - Journal of Nonlinear Mathematical Physics
SP  - 233
EP  - 242
VL  - 11
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2004.11.2.8
DO  - 10.2991/jnmp.2004.11.2.8
ID  - Hydon2004
ER  -