# Sine-Gordon equation

[Contributions to this section are sorely needed!]

The sine-Gordon equation

$\Box u = \sin(u)$

in R1 + 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 L2 or even L1 data.

It is also closely related to the sinh-Gordon equation

$\Box u = \sinh(u)$

and to Liouville's equation.