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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2006 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2006
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146102 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862714268993978368 |
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| author | Dorodnitsyn, V. |
| author_facet | Dorodnitsyn, V. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T17:50:08Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146102 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:50:08Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | On the Linearization of Second-Order Differential and Difference Equations Dorodnitsyn, V. |
| title | 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_short | On the Linearization of Second-Order Differential and Difference Equations |
| title_sort | on the linearization of second-order differential and difference equations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146102 |
| work_keys_str_mv | AT dorodnitsynv onthelinearizationofsecondorderdifferentialanddifferenceequations |