Integrable motion of two interacting curves, spin systems and the Manakov system
arXiv:1606.06598 · doi:10.1142/S0219887817501158
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 3-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.
12 pages