One half of these surfaces (cut in the middle) converge to the Pseudosphere

The formulas for the meridians of the surfaces of revolution with Gauss curvature
`K = -1`

are explicit and well known. To deform these surfaces, keeping
`K = -1`

, it is more
convenient to construct these surfaces from solutions of the Sine-Gordon equation (SGE).
For surfaces of revolution these SGE solutions can be obtained from the ODE
`q''(u) = sin(q(u))`

, with skew-symmetric solutions defined by initial conditions

`q(0) = 0`

`q'(0) = b > 0`

Then one can do the same as in the classical Dini deformation: define new solutions

`qn(u,v) := q(cosh(d)*u + sinh(d)*v)`

, with d the Dini parameter. The animation shows these surfaces.