Invariants and invariant description of second-order ODEs with three infinitesimal symmetries. I. (English) Zbl 1129.34029
There are four canonical forms for scalar second-order ordinary differential equations (ODEs) which admit three-dimensional Lie algebras in Lie’s classification in the complex domain. This paper gives an invariant description of one of the second-order equations which possess three symmetries. This is similar to what Lie and Tresse obtained for second-order equations with eight symmetries. It is anticipated that part II will provide criteria for the other equations in Lie’s classification. The authors chose to give a small sample of the literature in this otherwise actively researched area.
Reviewer: F. M. Mahomed (Johannesburg)
MSC:
| 34C14 | Symmetries, invariants of ordinary differential equations |
Software:
REDUCEReferences:
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