The Klein-Gordon Equation and Differential Substitutions of the Form v =φ( u , u x , u y )

Symmetry Integrability and Geometry-Methods and Applications

article

Mariya N. Kuznetsova¹  Aslı Pekcan²  Anatoliy V. Zhiber³ 

[1] Ufa State Aviation Technical University;Department of Mathematics, Istanbul University;Ufa Institute of Mathematics, Russian Academy of Science

关键词: Klein–Gordon equation;    dif ferential substitution;   

DOI  :  10.3842/SIGMA.2012.090

来源: National Academy of Science of Ukraine

【 摘 要 】

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 $\varphi_{u_x}\varphi_{u_y}\neq 0$ over the ring of complex-valued variables.

【 授权许可】

Unknown