Finding symmetries by incorporating initial conditions as side conditions

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...

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Bibliographic Details
Published in:European journal of applied mathematics 2008-12, Vol.19 (6), p.701-715
Main Author: GOARD, JOANNA
Format: Article
Language:English
Subjects:
Applied mathematics
Boundary value problems
Initial conditions
Invariants
Symmetry
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Summary: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.
ISSN:0956-7925
1469-4425
DOI:10.1017/S0956792508007705