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We pursue the question of multi-magnon dynamics, focusing on the simplestcase of magnons moving on RxS2 and working at the semiclassical level. Througha Pohlmeyer reduction, the problem reduces to another well known integrablefield theory, the sine-Gordon model, which can be exactly described through anN-body model of Calogero type. The two theories coincide at the level ofequations of motion, but physical quantities like the energies (of magnons andsolitons) and the associated phase shifts are different. We start from theequivalence of the two systems at the level of equations of motion and requirethat the new (string theory) model reproduces the correct magnon energies andthe phase shift, both of which differ from the soliton case. From thecomparison of energies we suggest a Hamiltonian, and from requiring the correctphase shift we are led to a nontrivial Poisson structure representing themagnons.

N-body Dynamics of Giant Magnons in RxS2