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 $v=φ(u,u_x,u_y)$ such that $φ_{u_x}φ_{u_y}\neq 0$ over the ring of complex-valued variables.
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