Is it possible to describe what are all the Bäcklund transforms of the pseudosphere at a high, intuitive level? The shapes in the aggregate set of all the transforms? Typically one sees images of very pseudosphere-like solutions , but I was surprised by this image:
(Image from Tim Hoffmann: “a Bäcklund transform of the … pseudosphere.”)
I admit I have not penetrated the Bobenko & Pinkall paper, which might explain this image:
“Discrete Surfaces with Constant Negative Gaussian Curvature and the Hirota Equation” (J. Diff. Geom., 1996, 43, pages 527–611). (ProjectEuclid PDF download.)
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