Differential Geometry and Integrability of the Hamiltonian System of a Closed Vortex Filament
Abstract
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 biHamiltonian 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.
 Publication:

arXiv eprints
 Pub Date:
 October 1995
 arXiv:
 arXiv:hepth/9510172
 Bibcode:
 1995hep.th...10172S
 Keywords:

 High Energy Physics  Theory;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 Title is changed ('a' is added). A mistake (absence of stating Flinearity condition of a skewadjoint op., Sect.4) is corrected. One reference is added. The other changes are minor. 12 pages, LaTeX