The Klein-Gordon Equation and Differential Substitutions of the Form $v=φ(u,u_x,u_y)$

Details The Klein-Gordon Equation and Differential Substitutions of the Form $v=φ(u,u_x,u_y)$ The Klein-Gordon Equation and Differential Substitutions of the Form $v=φ(u,u_x,u_y)$

2011-11-30

arxiv.org/abs/1111.7255v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

In this paper we present a complete classification of nonlinear differential
equations of the form $u_{xy} = f(u, u_x, u_y)$ reduced to the Klein-Gordon
equation $v_{xy} = F(v)$ by differential substitutions $v = \phi(u, u_x, u_y)$,
such that $\phi_{u_x}\phi_{u_y} \neq 0$.

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