Nonlinear Klein-Gordon equation
= Nonlinear Klein-Gordon equation
{title2=$\partial_t^2\phi-\partial_x^2\phi=f(\phi)$}
A local scalar nonlinearity preserves <Lorentz covariance> of the wave operator when the wave <speed> is one. If $f=F'$, the equation follows from $\mathcal L=(\partial_t\phi)^2/2-(\partial_x\phi)^2/2+F(\phi)$. The physical potential is $-F$, so its sign must be distinguished from the sign written in the <Lagrangian>.