Self-Invariant Contact Symmetries

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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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  -