Exponential nonlocal symmetries and nonnormal reduction of order
C. GéronimiMAPMO/URA CNRS 1803, Université and d'Orléans Départment de Mathématiques, BP 6759 45067 Orléans cedex 2, FranceMarc FeixMAPMO/URA CNRS 1803, Université and d'Orléans Départment de Mathématiques, BP 6759 45067 Orléans cedex 2, FranceP. G. L. LeachSchool of Mathematical and Statistical Sciences, University of Natal, Durban 4041, Republic of South Africa
2001en
ABI
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).
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