The Breather Surface:
The Breather surface is the surface of Gaussian
curvature minus one that corresponds to the
following solution of the Sine-Gordon equation:
q(u,v) := 4 * arctan( (aa / w) * (sin(w * v)) / (cosh(aa * u)) );
where:
w := sqrt( 1 - aa * aa);
See also: breather surface with parametric formula