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2001 J. Phys. A: Math. Gen. 34 10109-10117 doi: 10.1088/0305-4470/34/47/315
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Abstract. The conventional approach to double reduction of the order of an ordinary differential equation using Lie symmetries is via the normal subgroups of point symmetries. We show that, provided that one is prepared to use nonlocal symmetries, initial reduction by the nonnormal subgroup does not prevent the double reduction. We further illustrate our results with the general third-order equations invariant under the nonsolvable algebras, sl(2, R) (of which the Chazy equation is a noted example) and so(3).
PACS numbers: 02.20.−a, 02.30.Hq
Print publication: Issue 47 (30 November 2001) |
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