On the Linearization of Second-Order Differential and Difference Equations

This article complements recent results of the papers [J. Math. Phys. 41 (2000), 480; 45 (2004), 336] on the symmetry classification of second-order ordinary difference equations and meshes, as well as the Lagrangian formalism and Noether-type integration technique. It turned out that there exist no...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2006
1. Verfasser: Dorodnitsyn, V.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2006
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/146102
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:On the Linearization of Second-Order Differential and Difference Equations / V. Dorodnitsyn // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 11 назв. — англ.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-146102
record_format dspace
spelling Dorodnitsyn, V.
2019-02-07T13:18:42Z
2019-02-07T13:18:42Z
2006
On the Linearization of Second-Order Differential and Difference Equations / V. Dorodnitsyn // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 11 назв. — англ.
1815-0659
2000 Mathematics Subject Classification: 34C14; 34C20; 39A05; 65L12; 70H33
https://nasplib.isofts.kiev.ua/handle/123456789/146102
This article complements recent results of the papers [J. Math. Phys. 41 (2000), 480; 45 (2004), 336] on the symmetry classification of second-order ordinary difference equations and meshes, as well as the Lagrangian formalism and Noether-type integration technique. It turned out that there exist nonlinear superposition principles for solutions of special second-order ordinary difference equations which possess Lie group symmetries. This superposition springs from the linearization of second-order ordinary difference equations by means of non-point transformations which act simultaneously on equations and meshes. These transformations become some sort of contact transformations in the continuous limit.
The author thanks P. Winternitz and E. Ferapontov for helpful discussions and remarks. The author’s research was sponsored in part by the Russian Fund for Basic Research under the research project No 06-01-00707.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
On the Linearization of Second-Order Differential and Difference Equations
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title On the Linearization of Second-Order Differential and Difference Equations
spellingShingle On the Linearization of Second-Order Differential and Difference Equations
Dorodnitsyn, V.
title_short On the Linearization of Second-Order Differential and Difference Equations
title_full On the Linearization of Second-Order Differential and Difference Equations
title_fullStr On the Linearization of Second-Order Differential and Difference Equations
title_full_unstemmed On the Linearization of Second-Order Differential and Difference Equations
title_sort on the linearization of second-order differential and difference equations
author Dorodnitsyn, V.
author_facet Dorodnitsyn, V.
publishDate 2006
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description This article complements recent results of the papers [J. Math. Phys. 41 (2000), 480; 45 (2004), 336] on the symmetry classification of second-order ordinary difference equations and meshes, as well as the Lagrangian formalism and Noether-type integration technique. It turned out that there exist nonlinear superposition principles for solutions of special second-order ordinary difference equations which possess Lie group symmetries. This superposition springs from the linearization of second-order ordinary difference equations by means of non-point transformations which act simultaneously on equations and meshes. These transformations become some sort of contact transformations in the continuous limit.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/146102
citation_txt On the Linearization of Second-Order Differential and Difference Equations / V. Dorodnitsyn // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 11 назв. — англ.
work_keys_str_mv AT dorodnitsynv onthelinearizationofsecondorderdifferentialanddifferenceequations
first_indexed 2025-12-07T17:50:08Z
last_indexed 2025-12-07T17:50:08Z
_version_ 1850872753610031104