The system of a closed vortex filament is an integrable Hamiltonian one, namely, a Hamiltonian system with an infinite sequense of constants of motion in involution. An algebraic framework is given for the aim of describing differential geometry of this system. A geometrical structure related to the integrability of this system is revealed. It is not a bi-Hamiltonian structure but similar one. As a related topic, a remark on the inspection of J.Langer and R.Perline, J.Nonlinear Sci.1, 71 (1991), is given.
- Pub Date:
- October 1995
- High Energy Physics - Theory;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- Title is changed ('a' is added). A mistake (absence of stating F-linearity condition of a skew-adjoint op., Sect.4) is corrected. One reference is added. The other changes are minor. 12 pages, LaTeX