A new approach to the connections between moving curves and a family of complex KdV type systems

Abstract

In this paper, we give a new approach to the existence of a connection between the geometry of moving curves and the soliton equation for a family of complex KdV type systems by using two other classes of curve evolution in Euclidean space. As an application, we derive the soliton surfaces associated with the single soliton solutions of the given time evolution equations of the curvature function for the two-dimensional motion of the space curve.