The Klein-Gordon Equation and Differential Substitutions of the Form   $v=\varphi(u,u_x,u_y)$
  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 $\varphi_{u_x}\varphi_{u_y}\neq 0$ over the ring of complex-valued variables. 
Mariya N. Kuznetsova, Asli Pekcan and Anatoliy V. Zhiber
nlin.SI