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The projective geometric theory of systems of second-order differential equations: Straightening and symmetry theorems

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dc.contributor.author Aminova A.
dc.contributor.author Aminov N.
dc.date.accessioned 2018-09-18T20:16:24Z
dc.date.available 2018-09-18T20:16:24Z
dc.date.issued 2010
dc.identifier.issn 1064-5616
dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/138180
dc.description.abstract In the framework of the projective geometric theory of systems of differential equations, which is being developed by the authors, conditions which ensure that a family of graphs of solutions of a system of m second-order ordinary differential equations y→̈ = f→(t, y→, y→̇) with m unknown functions y1(t), ⋯ , ym(t) can be straightened (that is, transformed into a family of straight lines) by means of a local diffeomorphism of the variables of the system which takes it to the form z→″ 00 = 0 (straightens the system) are investigated. It is shown that the system to be straightened must be cubic with respect to the derivatives of the unknown functions. Necessary and sufficient conditions for straightening the system are found, which have the form of differential equations for the coefficients of the system or are stated in terms of symmetries of the system. For m = 1 the system consists of a single equation ÿ = f→(t, y, ẏ), and the tests obtained reduce to the conditions for straightening this equations which were derived by Lie in 1883. © 2010 RAS(DoM) and LMS.
dc.relation.ispartofseries Sbornik Mathematics
dc.subject Associated projective connection
dc.subject Projective geometric theory of systems of second-order ordinary differential equations
dc.subject Straightening theorems
dc.subject Symmetry group
dc.title The projective geometric theory of systems of second-order differential equations: Straightening and symmetry theorems
dc.type Article
dc.relation.ispartofseries-issue 5
dc.relation.ispartofseries-volume 201
dc.collection Публикации сотрудников КФУ
dc.relation.startpage 631
dc.source.id SCOPUS10645616-2010-201-5-SID77958582824


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  • Публикации сотрудников КФУ Scopus [24551]
    Коллекция содержит публикации сотрудников Казанского федерального (до 2010 года Казанского государственного) университета, проиндексированные в БД Scopus, начиная с 1970г.

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