Soliton curves in three-dimensional space forms

The localized induction hierarchy is the integrable hierarchy for the localized induction equation, a geometric evolution equation for space curves modeled on the motion of vortex filaments. A solution of the nth stationary equation associated to the localized induction hierarchy is called an nth soliton curve. In this paper, we consider soliton curves in simply-connected three-dimensional space forms. In particular, we give explicit expressions of nth soliton curves in terms of the natural curvatures.