The Klein-Gordon Equation and Differential Substitutions of the Form v=φ(u,ux,uy) - Kuznetsova, M.N.; Pekcan, A.; Zhiber, A.V. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
We present the complete classification of equations of the form uxy=f(u,ux,uy) and the Klein-Gordon equations vxy=F(v) connected with one another by differential substitutions v=φ(u,ux,uy) such that φuxφuy≠0 over the ring of complex-valued variables.