The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,u_x,u_y)
We present the complete classification of equations of the form $u_{xy}=f(u, u_x, u_y)$ and the Klein-Gordon equations $v_{xy}=F(v)$ connected with one another by differential substitutions $v=varphi(u,u_x,u_y)$ such that $varphi_{u_x}varphi_{u_y}eq 0$ over the ring of complex-valued variables.
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2012-11-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2012.090 |
| _version_ | 1811280819272024064 |
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| author | riya N. Kuznetsova Aslı Pekcan Anatoliy V. Zhiber |
| author_facet | riya N. Kuznetsova Aslı Pekcan Anatoliy V. Zhiber |
| author_sort | riya N. Kuznetsova |
| collection | DOAJ |
| description | We present the complete classification of equations of the form $u_{xy}=f(u, u_x, u_y)$ and the Klein-Gordon equations $v_{xy}=F(v)$ connected with one another by differential substitutions $v=varphi(u,u_x,u_y)$ such that $varphi_{u_x}varphi_{u_y}eq 0$ over the ring of complex-valued variables. |
| first_indexed | 2024-04-13T01:21:40Z |
| format | Article |
| id | doaj.art-ff0f291af2424501890b76d267815a9a |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-04-13T01:21:40Z |
| publishDate | 2012-11-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-ff0f291af2424501890b76d267815a9a2022-12-22T03:08:46ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592012-11-018090The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,u_x,u_y)riya N. KuznetsovaAslı PekcanAnatoliy V. ZhiberWe present the complete classification of equations of the form $u_{xy}=f(u, u_x, u_y)$ and the Klein-Gordon equations $v_{xy}=F(v)$ connected with one another by differential substitutions $v=varphi(u,u_x,u_y)$ such that $varphi_{u_x}varphi_{u_y}eq 0$ over the ring of complex-valued variables.http://dx.doi.org/10.3842/SIGMA.2012.090Klein-Gordon equationdifferential substitution |
| spellingShingle | riya N. Kuznetsova Aslı Pekcan Anatoliy V. Zhiber The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,u_x,u_y) Symmetry, Integrability and Geometry: Methods and Applications Klein-Gordon equation differential substitution |
| title | The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,u_x,u_y) |
| title_full | The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,u_x,u_y) |
| title_fullStr | The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,u_x,u_y) |
| title_full_unstemmed | The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,u_x,u_y) |
| title_short | The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,u_x,u_y) |
| title_sort | klein gordon equation and differential substitutions of the form v φ u u x u y |
| topic | Klein-Gordon equation differential substitution |
| url | http://dx.doi.org/10.3842/SIGMA.2012.090 |
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