Equivalence classes of second-order ordinary differential equations with only a three-dimensional Lie algebra of point symmetries and linearisation. (Q1406515)
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scientific article; zbMATH DE number 1974955
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Equivalence classes of second-order ordinary differential equations with only a three-dimensional Lie algebra of point symmetries and linearisation. |
scientific article; zbMATH DE number 1974955 |
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Equivalence classes of second-order ordinary differential equations with only a three-dimensional Lie algebra of point symmetries and linearisation. (English)
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4 September 2003
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The autor considers seven second-order ODEs, which are canonical representants for different ODE-classes in the case of exact 3 symmetries. These equations are investigated for linearisability by means of non-point transformations. The basic idea is to study these equations together with their parameters in the autonomous forms as first integrals of higher-order equations and then to get by symmetries some transformations. Connections to classical ODEs are presented, the equations are investigated with respect to Painlevé properties, too.
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second-order ordinary differential equations
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symmetry
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first integral
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closed form solution
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