On mapping moving curves to complex KdV-type equations for the Darboux triad in Euclidean space

Abstract

In this paper, we show a class of moving curves for the Darboux triad in Euclidean space that can be mapped onto complex KdV-type equations via the generalization of the Heisenberg ferromagnetic spin chain model. Furthermore, we give an approximation of the relationships with certain standard evolution equations.