  It is well known that sigma models in symmetric spaces accept equivalent
descriptions in terms of integrable systems such as the sine-Gordon equation
through Pohlmeyer reduction. In this paper, we study the mapping between known
solutions of the Euclidean O(3) non-linear sigma model, such as instantons,
merons and elliptic solutions that interpolate between the latter and solutions
of the Pohlmeyer reduced theory, namely the sinh-Gordon equation. It turns out
that instantons do not have a counterpart, merons correspond to the ground
state, while the class of elliptic solutions is characterized by a two to one
correspondence between solutions in the two descriptions.
