Nonlocal symmetries and reductions for some ordinary differential equations (Q1034469)
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scientific article; zbMATH DE number 5626842
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonlocal symmetries and reductions for some ordinary differential equations |
scientific article; zbMATH DE number 5626842 |
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Nonlocal symmetries and reductions for some ordinary differential equations (English)
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6 November 2009
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The author proposes finding nonlocal symmetries for an ODE by embedding it in auxiliary covering system with auxiliary dependent variables. Because the nonlocal symmetries of the ODEs are local symmetries of the associated auxiliary system, this result provides an algorithmic method for deriving such nonlocal symmetries. This allows using the computer for the usually rather lengthy calculations. Classes of ODEs are presented that have no Lie symmetry unless some conditions are satisfied but for which nonlocal symmetries are derived. These nonlocal symmetries allow reducing the order of these equations.
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conditional symmetry
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nonlocal symmetry
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ordinary differential equation
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