Searcharxiv⌕ Search

arXiv subjects

Norihito Sasaki

Publications and source records attributed to Norihito Sasaki.

3 recordsLinked to original sources
arXiv1996

Differential Geometry of the Vortex Filament Equation

Differential calculus on the space of asymptotically linear curves is developed. The calculus is applied to the vortex filament equation in its Hamiltonian description. The recursion operator generating the infinite sequence of commuting flows is shown to be hereditary. The system is shown to have a description with a Hamiltonian pair. Master symmetries are found and are applied to deriving an expression of the constants of motion in involution. The expression agrees with the inspection of Langer and Perline.

hep-th↗
arXiv1996

Differential Geometry and Integrability of the Hamiltonian System of a Closed Vortex Filament

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.

hep-th↗