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 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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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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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862672773516623872 |
|---|---|
| author | Kuznetsova, M.N. Pekcan, A. Zhiber, A.V. |
| author_facet | Kuznetsova, M.N. Pekcan, A. Zhiber, A.V. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T15:37:28Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148676 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:37:28Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| 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 | 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_short | 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) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148676 |
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