Sine-Gordon equation

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The sine-Gordon equation

in 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 or even data.

It is also closely related to the sinh-Gordon equation

and to Liouville's equation.