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Finding symmetries by incorporating initial conditions as side conditions

Published online by Cambridge University Press:  01 December 2008

JOANNA GOARD
JOANNA GOARD*
Affiliation:
University of Wollongong, School of Mathematics and Applied Statistics, Wollongong, NSW, Australia email: [email protected]
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Abstract

It is generally believed that in order to solve initial value problems using Lie symmetry methods, the initial condition needs to be left invariant by the infinitesimal symmetry generator that admits the invariant solution. This is not so. In this paper we incorporate the imposed initial value as a side condition to find ‘infinitesimals’ from which solutions satisfying the initial value can be recovered, along with the corresponding symmetry generator.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 19 , Issue 6 , December 2008 , pp. 701 - 715
Copyright
Copyright © Cambridge University Press 2008

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