C Géronimi et al 2001 J. Phys. A: Math. Gen. 34 10109 doi:10.1088/0305-4470/34/47/315
Exponential nonlocal symmetries and nonnormal reduction of order
C Géronimi1, M R Feix1 and P G L Leach2
Show affiliationsThe 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
- MSC
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22E40 Discrete subgroups of Lie groups (See also 20Hxx, 32Nxx)
- Subjects
- Dates
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Issue 47 (30 November 2001)
Received 7 September 2001
Published 16 November 2001
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Exponential nonlocal symmetries and nonnormal reduction of order
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