The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,ux,uy)
We present the complete classification of equations of the form uxy=f(u,ux,uy) and the Klein-Gordon equations vxy=F(v) connected with one another by differential substitutions v=φ(u,ux,uy) such that φuxφuy≠0 over the ring of complex-valued variables.
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2012 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2012
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148676 |
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| Zitieren: | The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,ux,uy) / M.N. Kuznetsova, A. Pekcan, A.V. Zhiber // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 20 назв. — англ. |
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Kuznetsova, M.N. Pekcan, A. Zhiber, A.V. 2019-02-18T17:48:22Z 2019-02-18T17:48:22Z 2012 The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,ux,uy) / M.N. Kuznetsova, A. Pekcan, A.V. Zhiber // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 35L70 DOI: http://dx.doi.org/10.3842/SIGMA.2012.090 https://nasplib.isofts.kiev.ua/handle/123456789/148676 We present the complete classification of equations of the form uxy=f(u,ux,uy) and the Klein-Gordon equations vxy=F(v) connected with one another by differential substitutions v=φ(u,ux,uy) such that φuxφuy≠0 over the ring of complex-valued variables. This paper is a contribution to the Special Issue “Symmetries of Dif ferential Equations: Frames, Invariants and Applications”. The full collection is available at http://www.emis.de/journals/SIGMA/SDE2012.html. This work is partially supported by the Russian Foundation for Basic Research (RFBR) (Grants 11-01-97005-Povolj’ie-a, 12-01-31208 mol-a). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,ux,uy) Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,ux,uy) |
| spellingShingle |
The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,ux,uy) Kuznetsova, M.N. Pekcan, A. Zhiber, A.V. |
| title_short |
The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,ux,uy) |
| title_full |
The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,ux,uy) |
| title_fullStr |
The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,ux,uy) |
| title_full_unstemmed |
The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,ux,uy) |
| title_sort |
klein-gordon equation and differential substitutions of the form v=φ(u,ux,uy) |
| author |
Kuznetsova, M.N. Pekcan, A. Zhiber, A.V. |
| author_facet |
Kuznetsova, M.N. Pekcan, A. Zhiber, A.V. |
| publishDate |
2012 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We present the complete classification of equations of the form uxy=f(u,ux,uy) and the Klein-Gordon equations vxy=F(v) connected with one another by differential substitutions v=φ(u,ux,uy) such that φuxφuy≠0 over the ring of complex-valued variables.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/148676 |
| citation_txt |
The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,ux,uy) / M.N. Kuznetsova, A. Pekcan, A.V. Zhiber // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 20 назв. — англ. |
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| first_indexed |
2025-12-07T15:37:28Z |
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