  We study classical string solutions on RxS^2 that correspond to elliptic
solutions of the sine-Gordon equation. In this work, these solutions are
systematically derived inverting Pohlmeyer reduction and classified with
respect to their Pohlmeyer counterparts. These solutions include the spiky
strings and other well-known solutions, such as the BMN particle, the GKP
string or the giant magnons, which arise as special limits, and reveal many
interesting features of the AdS/CFT correspondence. A mapping of the physical
properties of the string solutions to those of their Pohlmeyer counterparts is
established. An interesting element of this mapping is the correspondence of
the number of spikes of the string to the topological charge in the sine-Gordon
theory. In the context of the sine-Gordon/Thirring duality, the latter is
mapped to the Thirring model fermion number, leading to a natural
classification of the solutions to fermionic objects and bosonic condensates.
Finally, the convenient parametrization of the solutions, enforced by the
inversion of the Pohlmeyer reduction, facilitates the study of the string
dispersion relation. This leads to the identification of an infinite set of
trajectories in the moduli space of solutions, where the dispersion relation
can be expressed in a closed form by means of some algebraic operations,
arbitrarily far from the infinite size limit.
