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Self-Invariant Contact Symmetries

Hydon, Peter E. (2004) Self-Invariant Contact Symmetries Journal of Non-linear Mathematical Physics, 11 (2). pp. 233-242.


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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

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Hydon, Peter
Date : 1 May 2004
DOI : 10.2991/jnmp.2004.11.2.8
Additional Information : Published in Journal of Nonlinear Mathematical Physics, 11, 233-242. © Atlantis Press. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:41
Last Modified : 31 Oct 2017 14:02

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