describes the surfaces of constant negative curvature.

These pictures are the surfaces that correspond to soliton
and breather solutions of this equation.

In my paper "Sine-Gordon equation and representations of
$\hat sl_2$", I show that the hidden symmetries of the
sine-Gordon equation are given by the Kac-Moody
algebra $\hat sl_2$ and obtain the soliton solutions
via the Kac-Moody group action on the space of
differential operators.

The images were generated with Richard Palais' 3DFilmstrip program by Robert Milson (Dalhousie University).