Discrete Curve. Min Minkowski Space Movement And Discrete Integrable Equations

The discrete modified Heisenberg ferromagnet(MHF) models a(?)e the important in-tegrable equations. It is known that they are gauge equivalent to the discrete nonlinear schro|¨dinger(DNLS) equation. In this paper, we will present their geometric equivalence. The motion of a discrete curve in Minkowski space is first introduced. Then by identifying the spin vector of HF models with the unit vectors of discrete curve, respectively, we obtain the corresponding DNLS.