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The '''sine-Gordon equation'''

<center><math>\Box u = \sin(u)</math></center>

in <math>R^{1+1}</math> 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 <math>L^2</math> or even <math>L^1</math> data.

It is also closely related to the '''sinh-Gordon equation'''

<center><math>\Box u = \sinh(u)</math></center>

and to [[Liouville's equation]].

[[Category:Integrability]]
[[Category:wave]]
[[Category:Equations]]