Squared eigenfunctions and linear stability properties of closed vortex filaments

摘要: We develop a general framework for studying the linear stability of closed solutions vortex filament equation (VFE), based on correspondence between VFE and nonlinear Schrodinger (NLS) provided by Hasimoto map, construction linearized equations in terms NLS squared eigenfunctions. In particular, we show that differential map is one-to-one curve variations perturbations potentials induced apply this to filaments associated with periodic finite-gap genus one case, cnoidal characterize their knot type.