2016/06/28 by Thomas Ivey, Ivey, Thomas, Stéphane Lafortune +1
Mathematics · Physics and Astronomy · #35Q35 #35Q55 #37K20 #37K45 #Advanced Mathematical Physics Problems #Cold Atom Physics and Bose-Einstein Condensates #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.1606.08739
openalex publication_date 2016/06/28 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
The Vortex Filament Equation (VFE) is part of an integrable hierarchy of\nfilament equations. Several equations part of this hierarchy have been derived\nto describe vortex filaments in various situations. Inspired by these results,\nwe develop a general framework for studying the existence and the linear\nstability of closed solutions of the VFE hierarchy. The framework is based on\nthe correspondence between the VFE and the nonlinear Schr "odinger (NLS)\nhierarchies. Our results show that it is possible to establish a connection\nbetween the AKNS Floquet spectrum and the stability properties of the solutions\nof the filament equations. We apply our machinery to solutions of the filament\nequation associated to the Hirota equation. We also discuss how our framework\napplies to soliton solutions.\n