Breather Surface

    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