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Integrable spin systems are an important subclass of integrable (soliton)nonlinear equations. They play important role in physics and mathematics. Atpresent, many integrable spin systems were found and studied. They are relatedwith the motion of 3-dimensional curves. In this paper, we consider a model oftwo moving interacting curves. Next, we find its integrable reduction relatedwith some integrable coupled spin system. Then we show that this integrablecoupled spin system is equivalent to the famous Manakov system.

Integrable motion of two interacting curves, spin systems and the Manakov system