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Lie-Backlund symmetries of submaximal order of ordinary differential equationsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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##### Responsible organisation

PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2002 (English)In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, 155-166 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

DORDRECHT: KLUWER ACADEMIC PUBL , 2002. 155-166 p.
##### Keyword [en]

Lie-Backlund symmetries, ordinary differential equations, symmetries of submaximal order
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:bth-8162ISI: 000174933300005Local ID: oai:bth.se:forskinfo6B4B9401B7391437C12575B0002107CFOAI: oai:DiVA.org:bth-8162DiVA: diva2:835851
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt375",{id:"formSmash:j_idt375",widgetVar:"widget_formSmash_j_idt375",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt381",{id:"formSmash:j_idt381",widgetVar:"widget_formSmash_j_idt381",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt387",{id:"formSmash:j_idt387",widgetVar:"widget_formSmash_j_idt387",multiple:true});
Available from: 2012-09-18 Created: 2009-05-08 Last updated: 2015-06-30Bibliographically approved

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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