2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/197811We explicitly construct a large class of finite-volume two-magnon string solutions moving on R x S^2. In particular, by making use of the relationship between the O(3) sigma model and sine-Gordon theory we are able to find solutions corresponding to the periodic analogues of magnon scattering and breather-like solutions. After semi-classically quantizing these solutions we invert the implicit expressions for the excitation energies in certain limits and find the corrections for the multi-magnon states. For the breather-like solutions we express the energies directly in terms of the action variable whereas for the scattering solution we express the result as a combination of corrections to the dispersion relation and to the scattering phase.45pages, 7figures, v2: simplified expressions for periods and angular momenta when elliptic modulus is greater than one, references added, typos correctedHigh Energy Physics - Theorytext