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: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
National Academy of Science of Ukraine
2012-11-01
|
| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2012.090 |