Pohlmeyer reduction and Darboux transformations in Euclidean worldsheet AdS₃

Pohlmeyer reduction has been instrumental both in the program for computing gluon scattering amplitudes at strong coupling, and more recently in the progress towards semiclassical three-point correlators of heavy operators in AdS/CFT. After a detailed review of the method, we combine it with Darboux and Crum transformations in order to obtain a class of string solutions corresponding to an arbitrary number of kinks and breathers of the elliptic sinh-Gordon equation. We also use our construction in order to identify the previously found dressed giant gluon with the single breather solution.