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This paper studies giant magnons in AdS_4 x CP^3 using both the stringsigma-model and the algebraic curve. We complete the dictionary of solutions byfinding the dyonic generalisation of the CP^1 string solution, which matchesthe `small' giant magnon in the algebraic curve, and by pointing out that thesolution recently constructed by the dressing method is the `big' giant magnon.We then use the curve to compute finite-J corrections to all cases, which forthe non-dyonic cases always match the AFZ result. For the dyonic RP^3 magnon werecover the S^5 answer, but for the `small' and `big' giant magnons we obtainnew corrections.

Dyonic Giant Magnons in CP^3: Strings and Curves at Finite J