Integrable motion of two interacting curves, spin systems and the Manakov system
Exactly Solvable and Integrable Systems
2017-06-07 v3
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.
Keywords
Cite
@article{arxiv.1606.06598,
title = {Integrable motion of two interacting curves, spin systems and the Manakov system},
author = {Akbota Myrzakul and Ratbay Myrzakulov},
journal= {arXiv preprint arXiv:1606.06598},
year = {2017}
}
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12 pages