  This paper is concerned with a class of approximate non-linear
transformations that compress solutions of the (generalized) sinh-Gordon
equation into parametrically small regions in two-dimensional spacetime. Given
the sinh-Gordon field near a time-slice, a long Nambu-Goto string can be
constructed in three-dimensional anti-de Sitter space. The string is then
approximated to arbitrary accuracy by a slightly smoothed piecewise linear
string of N segments. The corresponding sinh-Gordon field has a comb-like
structure and its size is controlled by the amount of smoothing applied to the
segmented string. In a (singular) large-N limit, the transformation commutes
with time evolution. As an example, a static cosh-Gordon solution is discussed
in detail. The corresponding smooth and segmented string solutions are obtained
and the compressed cosh-Gordon potential is investigated.
