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Lie-Backlund symmetries of submaximal order of ordinary differential equations
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2002 (English)In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, 155-166 p.Article in journal (Refereed) Published
Abstract [en]

It is well known that the maximal order of Lie-Backlund symmetries for any nth-order ordinary differential equation is equal to n-1, and that the whole set of such symmetries forms an infinite-dimensional Lie algebra. Symmetries of the order pless than or equal ton - 2 span a linear subspace (but not a subalgebra) in this algebra. We call them symmetries of submaximal order. The purpose of the article is to prove that for n less than or equal to 4 this subspace is finite-dimensional and it's dimension cannot be greater than 35 for n=4, 10 for n=3 and 3 for n=2. In the case n=3 this statement follows immediately from Lie's result on contact symmetries of third-order ordinary differential equations. The maximal values of dimensions are reached, e.g., on the simplest equations y((n))=0.

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Keyword [en]
Lie-Backlund symmetries, ordinary differential equations, symmetries of submaximal order
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URN: urn:nbn:se:bth-8162ISI: 000174933300005Local ID: diva2:835851
Available from: 2012-09-18 Created: 2009-05-08 Last updated: 2015-06-30Bibliographically approved

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