Notes on dispersionful and dispersionless vortex filament equations in   1+1 and 2+1 dimensions
  The vortex filament equations (VFE) in 1+1 and 2+1 dimensions are considered. Some of these equations are integrable. Also the VFE with potentials and with self-consistent potentials are presented. Finally several examples of integrable dispersionless VFE (dVFE) are considered. 
R. Myrzakulov