Characterization of Symmetry Properties of First Integrals for Submaximal Linearizable Third-Order ODEs

K. S. Mahomed and E. Momoniat

Mathematical Problems in Engineering, 2013, vol. 2013, 1-9

Abstract:

The relationship between first integrals of submaximal linearizable third-order ordinary differential equations (ODEs) and their symmetries is investigated. We obtain the classifying relations between the symmetries and the first integral for submaximal cases of linear third-order ODEs. It is known that the maximum Lie algebra of the first integral is achieved for the simplest equation and is four-dimensional. We show that for the other two classes they are not unique. We also obtain counting theorems of the symmetry properties of the first integrals for these classes of linear third-order ODEs. For the 5 symmetry class of linear third-order ODEs, the first integrals can have 0, 1, 2, and 3 symmetries, and for the 4 symmetry class of linear third-order ODEs, they are 0, 1, and 2 symmetries, respectively. In the case of submaximal linear higher-order ODEs, we show that their full Lie algebras can be generated by the subalgebras of certain basic integrals.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:214872

DOI: 10.1155/2013/214872

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