Knot types, Floquet spectra, and finite-gap solutions of the vortex filament equation

Using the connection between closed solution curves of the vortex filament equation and the periodic problem for the nonlinear Schrödinger equation (NLS), we investigate the possibility of relating the knot types of finite-gap solution to the Floquet spectra of the corresponding NLS potentials, in the special case of small amplitude curves close to multiply-covered circles.