Integrability of Klein–Gordon Equations
Integrability of Klein–Gordon Equations
Using the Painlevé test, it is shown that the only integrable nonlinear Klein–Gordon equations $u_{xt} = f(u)$ with f a linear combination of exponentials are the Liouville, sine-Gordon (or sink-Gordon) and Mikhailov equations. In particular, the double sine-Gordon equation is not integrable.