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.
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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 |
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| Online Access: | http://dx.doi.org/10.3842/SIGMA.2012.090 |
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doaj-ff0f291af2424501890b76d267815a9a2020-11-25T01:36:19ZengNational 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
riya N. Kuznetsova Aslı Pekcan Anatoliy V. Zhiber |
| 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 |
| author_facet |
riya N. Kuznetsova Aslı Pekcan Anatoliy V. Zhiber |
| author_sort |
riya N. Kuznetsova |
| title |
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_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_sort |
klein-gordon equation and differential substitutions of the form v=φ(u,u_x,u_y) |
| publisher |
National Academy of Science of Ukraine |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| issn |
1815-0659 |
| publishDate |
2012-11-01 |
| 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. |
| topic |
Klein-Gordon equation differential substitution |
| url |
http://dx.doi.org/10.3842/SIGMA.2012.090 |
| work_keys_str_mv |
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