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Discrete point symmetries of ordinary differential equations

Hydon, P. E. (1998) Discrete point symmetries of ordinary differential equations Proceedings of the Royal Society of London A, 454. pp. 1961-1972.


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This paper describes a method that enables the user to construct systematically the set of all discrete point symmetries of a given ordinary differential equation (ODE) of order two or greater, provided that the ODE has at least a one-parameter Lie group of point symmetries. The method is easy to use, and is based upon Lie's method of constructing continuous symmetries. The calculations are simple, and computer algebra is not usually required. Various examples are used to illustrate the method. The paper concludes with a proof that every ODE whose Lie group of point symmetries is isomorphic to the unimodular group has at least four inequivalent real discrete point symmetries.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Hydon, P.
Date : 8 July 1998
Uncontrolled Keywords : differential equations, symmetry methods, constructive techniques, equivariant bifurcation theory, boundary-value problems, computer algebra
Additional Information : Published in Proceedings of the Royal Society of London A, 454, 1961-1972. © 1998 The Royal Society.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:41
Last Modified : 23 Sep 2013 18:33

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