The Klein–Gordon Equation and Differential Substitutions of the Form $v=\varphi(u,u_x,u_y)$

Mariya N. Kuznetsova ; Asli Pekcan ; Anatoliy V. Zhiber

Symmetry, integrability and geometry: methods and applications, Tome 8 (2012)

Résumé

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.

Détail

Keywords: Klein–Gordon equation; differential substitution.

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