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


Kuznetsova M. N., Pekcan A., Zhiber A. V.

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, vol.8, 2012 (SCI-Expanded) identifier identifier

Abstract

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 = phi(u, u(x,) u(y)) such that phi(ux)phi(uy) not equal 0 over the ring of complex-valued variables.