Notes on dispersionful and dispersionless vortex filament equations in 1+1 and 2+1 dimensions

Abstract

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.

11 pages, no figures

References in corpus (3)

• Closed curves in R^3: a characterization in terms of curvature and torsion, the Hasimoto map and periodic solutions of the Filament Equation
• Approximation theorem for the self-focusing Nonlinear Schrödinger Equation and for the periodic curves in ${\mathbf{R}}^3$
• Some notes on Ishimori's magnet model