N-solitons on a vortex filament

We describe a purely algebraic algorithm for finding, in the localized induction approach, three-dimensional vortex motion corresponding to the N-soliton solution of the nonlinear Schrödinger equation. The method used relies essentially up-on the geometric approach to soliton systems and consists in the construction of the corresponding soliton surfaces. For N = 0 and N = 1 we recover the straight line and Hasimoto vortex, respectively, while for N = 2 the algorithm gives a new vortex motion, of higher complexity, which is, presumably, an analytic expression for some scattering phenomena along vortices recently discovered by Browand and Hopfinger.