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

Abstract

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