Sine-Gordon equation

[Contributions to this section are sorely needed!]

The sine-Gordon equation

$\Box u=\sin(u)$

in $R^{1+1}$ arises in the study of optical pulses, or from the Scott model of a continuum of pendula hanging from a wire. It is a completely integrable equation, and has many interesting solutions, including "breather" solutions.

Because the non-linearity is bounded, GWP is easily obtained for $L^{2}$ or even $L^{1}$ data.

It is also closely related to the sinh-Gordon equation

$\Box u=\sinh(u)$

and to Liouville's equation.